Nicolae Popescu
Encyclopedia
Nicolae Popescu was a Romanian mathematician
and Emeritus Professor. Popescu was elected a Member of the Romanian Academy
in 1992. He is best known for his contributions to Algebra
and the theory of Abelian categories. Since 1964 and until 2007 he collaborated on the characterization of abelian categories with the well-known French mathematician Pierre Gabriel. His areas of expertise were: Category theory
, Abelian categories
with Applications to Rings
and Modules
, adjoint functors, limits
/colimits,, Theory of Sheaves, Theory of Rings
, Fields
and Polynomials, and Valuation Theory
; he also has interests and published in the following areas: Algebraic Topology
, Algebraic Geometry
, Commutative Algebra
, K-Theory
, Class-Field theory
, and Algebraic Function Theory
. He published between 1962 and 2008 more than 102 papers in peer-reviewed, mathematics journals, several monographs on the theory of sheaves, and also six books on abelian category theory
and abstract algebra
. In a Grothendieck-like, energetic style, he initiated and provided scientific leadership to several seminars on category theory, sheaves and abstract algebra which resulted in a continuous stream of high-quality mathematical publications in international, peer-reviewed mathematics journals by several members participating in his Seminar series. His book Abelian Categories with Applications to Rings and Modules continues to provide valuable information to mathematicians around the world. His latest contributions have also branched into valuation and number theory. He has published over 100 original, peer-reviewed articles in mathematics, mostly in category theory
, algebraic geometry
, and Galois and number theory
.
degree in mathematics in 1964, and his Ph.D.
degree in mathematics in 1967, both at the University of Bucharest
. He was awarded a D. Phil. degree (Doctor Docent) in 1972 by the University of Bucharest.
In 2009 he carried out mathematics studies at the Institute of Mathematics of the Romanian Academy in the Algebra research group and also had international collaborations on three continents. One found from conversations with former Academician Nicolae Popescu that he shared many moral, ethical and religious values with another famous mathematician French-German-Jewish Alexander Grothendieck
who visited the School of Mathematics in Bucharest in 1968. Like Grothendieck
he had a long-standing interest in category theory, number theory, practicing Yoga, and supporting promising young mathematicians in his fields of interest. He also supported the early developments of category theory applications in relational biology
and mathematical biophysics/mathematical biology
.
, which institute was ruthlessly eliminated by former dictator and president of S.R. Romania, Nicolae Ceaușescu
, in 1976 for reasons related to his daughter Zoe Ceaușescu who was 'hired' by the Mathematics Institute in Bucharest two years before.
2. Diferențiale generalizate, Comunicările Acad. R.S.R., Tom 13, Nr. 6 (1963), 523-528. (with C. Bănică) (Generalized Differential Functions).
3. Quelques considérations sur l'exactitude des foncteurs, Bull. Math. Soc. Sci. Math. Phis. de la R. P. R. 7 (1963), 144-147. (with C. Bănică)
4. Modules à différentielle généralisée, Rev. Roumaine Math. Pures Appl. Tome IX, Nr. 6 (1964). 549-559.
5. Module cu diferentiala generalizata, Stud. Cerc. Mat. Tom 16, Nr. 6. (1964), 791-800.
6. La structure des modules injectifs sur an anneau á idéal principal, Bull. Math. de la Soc. Sci. Math. Phys. de la RPR Tome 8 (56), Nr. 1-2 (1964), 67-73. (with A. Radu)
7. Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C. R. Acad. Sci. Paris 258 (1964), 4188-4191. (with Pierre Gabriel)
8. Asupra categoriilor preabeliene (On pre-Abelian categories), Stud. Cerc. Mat. Tom 17 (1965), 563–575 (with C. Bănică)
9. Sur les catégories preabéliens, Rev. Roumaine Math. Pures Appl., 10(1965), 621-633. (with C. Bănică)
10. La localisation pour des sites, Rev. Roumaine Math. Pures Appl. 10 (1965), 1031-1044.
11. Categorii cat (Quotient categories), Stud. Cerc. Mat. Tom 17, Nr. 6 (1965), 951-985. (with C. Bănică)
12. Sur la structure des objets de certaines catégories abéliennes, C.R. Acad. Sci. Paris, t. 262(1966), 1295-1297. (with C. Năstăsescu)
13. Elemente de teoria fasciculelor I, (Elements of the theory of sheaves, I), Stud. Cerc. Mat. (1966) 267-296.
14. Elemente de teoria fasciculelor II (Elements of the theory of sheaves, I), Stud. Cerc. Mat. (1966) 407-456.
15. Elemente de teoria fasciculelor III (Elements of the theory of sheaves, III), Stud. Cerc. Mat. (1966) 547-583.
16. Elemente de teoria fasciculelor IV (Elements of the theory of sheaves, IV), Stud. Cerc. Mat. (1966) 647-669.
17. Morphismes et co-morphismes des topos abéliens, Bull. Math. de la Soc. Sci. Math. de la R.S.R. Tom 10 (58) Nr. 4 (1966), 319-328. (with A. Radu)
18. Elemente de teoria fasciculelor V (Elements of the theory of sheaves, V), Stud. Cerc. Mat. (1966) 945-991.
19. Quelques observations sur les topes abéliens, Rev. Roumaine Math. Pures Appl. 12 (1967), 553-563. (with C. Năstăsescu)
20. Théorie générale de la décomposition, Rev. Roum Math. Pures et Appl. Tome XII, Nr. 9 (1967), 1365-1371.
21. Elemente de teoria fasciculelor VI (Elements of the theory of sheaves, VI), Stud. Cerc. Mat. (1967) 205-240.
22. Anneaux semi-artiniens, Bull. Soc. Math. France 96 (1968), 357-368. (with C. Năstăsescu).
23. Sur les epimorphismes plats d'anneaux, C.R. Acad. Sci. Paris 268 (1969), 376-379. (with T. Spîrcu).
24. On the localization ring of ring, J. Algebra 15 (1970), 41-56. (with C. Năstăsescu)
25. Quelques observations sur les Épimorphismes plats (à Gauche) d’Anneaux, J. Algebra Vol. 16, Nr.1 (1970), 40-59. (with T. Spircu)
26. Sur les quasi-ordres (à gauche) dans un anneau, J. Algebra 17, Nr. 4 (1971), 474-481. (with D. Spulber)
27. Les anneaux semi-noethériens, C.R. Acad. Sci. Paris t. 272 (1971), 1439-1441.
28. Le spectre à gauche d'un anneau, J. Algebra 18, No. 2 (1971), 213-228.
29. Sur les C. P. anneaux, C.R. Acad. Sci. Paris t. 272 (1971), 1493-1496.
30. Théorie primaire de la décomposition dans les anneaux semi-noethériens, J. Algebra Vol. 23, No. 3 (1972), 482-492.
31. Quelques considérations sur les anneaux semi-artiniens commutatifs, C. R. Acad. Sci. Paris t. 276 (1973), 1545-1548.
32. Some remarks about semi-Artinian rings, Rev. Roumaine Math. Pures Appl. Tome XVIII, Nr. 9 (1973), 1413-1422. (with C. Vraciu)
33. Exemple de inele semi-artiniene, (Examples of semi-Artinian rings), Stud. Cerc. Math. Tom 26, Nr. 8 (1974), 1153-1157. (with T. Spîrcu)
34. Permanence Theorems for semi-artinian rings, Rev. Roumaine Math. Pures Appl. XXI, Nr.2 (1976), 227-231. (with T. Spircu)
35. Sur l'anneau des quotients d'un anneau noethérien (à droite) par rapport au système localisant associe à un idéal bilatéral premier, C.R. Acad. Sci. Paris.
36. Sur la structure des anneaux absolument plats commutatifs, J. Algebra Vol. 40, No. 2 (1976), 364-383. (with C. Vraciu)
37. Some remarks about the regular ring associated to a commutative ring, Rev. Roumaine Math. Pures et Appl. Tome XXIII (1978), 269-277. (with C. Vraciu)
38. Sur la sous-catégorie localisante associée à un idéal bilatéral premier dans un anneau noethérien (à droite), Rev. Roumaine Math. Pures Appl. Tome XXVI, Nr. 7 (1981), 1033-1042.
39. Sur un problème d'Arens et Kaplansky concernant la structure de quelques anneaux absolument plats commutatifs, Rev. Roumaine Math. Pures Appl., Tome. XXVII, Nr. 8 (1982), 867-874. (with C. Vraciu)
40. Sur une classe de polynômes irréductibles, C.R. Acad. Sci. Paris, t. 297 (1983), 9-11.
41. On a class of Prüfer domains, Rev. Roum. Math. Pures et Appl. Tome XXIX, Nr. 9 (1984), 777-786.
42. Galois Theory of permitted extensions of commutative regular rings, Bull. Math. Soc. Sci. Math. R.S. Roumanie, Tome 29 (77), nr. 2 (1985), 121-135. (with C. Vraciu)
43. On Dedekind Domains in Infinite Algebraic Extensions, Rend. Sem. Mat. Univ. Padova, Vol. 74 (1985), 39-44. (with C. Vraciu)
44. Local class field theory. I, (Romanian, Teoria locală a corpului claselor. I,. English summary), Stud. Cerc. Mat. 37 (1985), no. 4, 295–312.
45. On subfields of k(x), Red. Sem. Mat. Univ. Padova, Vol. 75 (1986), 257-273. (with V. Alexandru)
46. Local class field theory. II. (Romanian, Teoria locală a corpului claselor. I), Stud. Cerc. Mat. Tom 38, (1986), No.2, 107-138.
47. On a problem of Nagata in valuation theory, Rev. Roumaine Math. Pures Appl. Tome XXXI, Nr. 7 (1986), 639-641.
48. On a class of intermediate Subfields, Stud. Cerc. Mat., Tom 39, Nr. 2 (1987), p. 156-162. (with E.L. Popescu)
49. Sur une clase de prolongements à K(X) d'une valuation sur un corps K, Rev. Roumaine Math. Pures Appl., Tome XXXIII (1988), 393-400. (with V. Alexandru)
50. A theorem of characterization of residual transcendental extensions of a valuation, J. Math. Kyoto Univ. Vol. 28, Nr. 4 (1988), 579-592. (with V. Alexandru and A. Zaharescu)
51. Sur la définition des prolongements résiduels transcendents d'une valuation sur un corps K à K(X), Bull. Math. Soc. Sci. Math. Roumanie, Tome. 33 (1989), 257-264. (with E. L. Popescu)
52. Minimal pairs of definition of a residual transcendental extension of a valuation, J. Math. Kyoto, Univ., Vol. 30, Nr. 2 (1990), 207-225. (with V. Alexandru and A. Zaharescu)
53. All valuations on K(X), J. Math. Kyoto Univ., Vol. 30, Nr. 2 (1990), 281-296. (with V. Alexandru and A. Zaharescu)
54. On the residual transcendental extensions of a valuation. Key polynomials and augmented valuation, Math. Tsukuba Univ. Vol. 15, No.1 (1991), 57-78. (with E.L. Popescu)
55. A characterization of Generalized-Dedekind Domains, Bull. Math. de la Soc. Sci. Math. de Roumanie, Tome 35 (83), Nr.1-2 (1991), 139-141. (with E. L. Popescu)
56. On the Extension of Valuations on a Field K to K(X) – I, Red. Sem. Mat. Univ. Padova, Vol. 87 (1992), 151-168. (with C. Vraciu)
57. Some elementary remarks about n-local fields, Rend. Sem. Math. Univ. Padova, Vol. 91 (1994), 17-28 (with V. Alexandru)
58. On a class of valuations on K(X), 11th National Conference of Algebra, Constanta, 1994, An. St. Univ. Ovidius Constantza, Seria: Mat. Vol. II (1994), 120-136. [53] (with A. Zaharescu)
59. Sur une classe d'anneaux qui généralisent les anneaux de Dedekind, J. Algebra, Vol.173, (1995), 44-66. (with M. Fontana)
60. On the structure of the irreducible polynomials over local fields, J. Number Theory, Vol. 52, No. 1 (1995), 98-118. (with A. Zaharescu)
61. Sur une classe d’anneaux de Prüfer avec groupe de classes de torsion, Comm. Algebra 23 (1995), no. 12, 4521–4533. (with M. Fontana)
62. Completion of r. t. extension of a local field (I), Math. Z., Vol. 221 (1996), 675-682. (with V. Alexandru and A. Popescu)
63. On the extension of a valuation on a Field K to K(X) - II, Rend. Sem. Mat, Univ. Padova, Vol. 96 (1996), 1-14. (with C. Vraciu)
64. On a class of Domains having Prüfer integral closure: The FQR-domains, Commutative ring theory (Fès, 1995), 303-312, Lecture Notes in Pure and Appl. Math. Vol. 185, Dekker, New York, 1997. (with M. Fontana)
65. On the main invariant of an element over a local field, Portugalia Mathematica, Vol. 54, Fasc. 1 (1997), 73-83. (with A. Zaharescu)
66. On the closed subfields of Cp, J. Number Theory, Vol. 68, No. 2 (1998), 131-150. (with V. Alexandru and A. Zaharescu)
67. The Lüroth's Theorem for some complete fields, in Abelian Groups, Module Theory and Topology, Editors Dikranian-Salce, Marcel Dekker Inc., 1998, 55-58. (with V. Alexandru)
68. Abelian groups, module theory, and topology (Padua, 1997), 55–58, Lecture Notes in Pure and Appl. Math., 201, Dekker, New York, 1998.
69. Completion of r. t. extensions of local fields (II), Rend. Sem. Mat. Univ. Padova, Vol. 100 (1998). (with V. Alexandru and A. Popescu)
70. On the roots of a class of lifting polynomials, Fachbereich Math. Univ. Hagen, Band 63 (1998), 586-600. (with A. Zaharescu)
71. Invertible ideals and Picard group of generalized Dedekind domains, J. Pure and Appl. Alg., Vol 135, Nr. 3 (1999), 237-251. (with S. Gabelli)
72. The generating degree of Cp, Canad. Math. Bull. Vol. 44 (1), 2001, 3-11. (with V. Alexandru and A. Zaharescu)
73. Trace on Cp, J. Number Theory 88 (2001), Nr.1, 13-48. (with V. Alexandru and A. Zaharescu)
74. Spectral norms on valued fields, Math. Z., Vol. 238 (2001), 101-114. (with V. Pasol and A. Popescu)
75. Metric invariants in B+dR associated to differential operators, Rev. Roumaine Math. Pures Appl. XLVI, Nr. 5 (2001), 552-564. (with V. Alexandru and A. Zaharescu)
76. Completion of the Spectral extensions of p-adic valuation, Rev. Roum. Math. Pures et Apll, Vol. XLVI, Nr. 6 (2001), 805-817. (with E. L. Popescu and C. Vraciu)
77. Nagata Transform and Localizing Systems, Comm. in Algebra, 30(5), (2002), 2297-2308. (with Marco Fontana)
78. Chains of metric invariants over a local field, Acta Arithmetica, 103.1 (2002), 27-40. (with A. Popescu, M. Vajaitu and A. Zaharescu)
79. Universal property of the Kaplansky ideal transform and affineness of Open Subsets, J. Pure and Appl. Alg., 173, (2002), 121-134. (with Marco Fontana)
80. Total valuation rings of K(X, σ) containing K, Communications in Algebra, Volume 30, Number 11 (2002), 5535 – 5546. (with S. Kobayashi, H. Marubayashi and C. Vraciu)
81. On minimal pairs and residually transcendental extensions of valuations (Mathematika, 49 (2002), 93-106. (with S. Khanduja and K.W. Roggenkamp)
82. Total valuation rings of Ore extensions, Result. Math., 43 (2003), 373-379. (with S. Kobayashi, H. Marubayashi, C. Vraciu and G. Xie)
83. Galois action on plane compacts, Proceedings of the 35th Symposium on Ring Theory and Representation Theory (Okayama, 2002), 113–120, Symp. Ring Theory Represent Theory Organ. Comm., Okayama, 2003.
84. Transcendental divisors and their critical functions, Manuscripta Math., 110 (4), (2003), 527-541. (with A. Popescu and A. Zaharescu)
85. Trace Series on Q ̃K, Result. Math., 43 (2003), 331-341 (with A. Popescu and A. Zaharescu)
86. Metric invariants over Henselian valued Fields, J. Algebra, 266 (1), (2003), 14-26. (with A. Popescu and A. Zaharescu)
87. Galois structures on plane compacts, J. Algebra, 270, (2003), 238-248. (with A. Popescu and A. Zaharescu)
88. Good elements and metric invariants in B+dR, J. Math. Kyoto Univ, vol 43, Nr. 1 (2003), 125-137. (with V. Alexandru and A. Zaharescu)
89. A representation theorem for a class of rigid analytic functions, J. Th. Nombres Bordeaux, 15 (2003), 639-650. (with V. Alexandru and A. Zaharescu)
90. A characterization of completion of the spectral extension of p-adic valuation, World Conference on 21st Century Mathematics 2004, 157–161, Sch. Math. Sci.G.C. Univ., Lahore, 2004. (with E. L Popescu)
91. On afine subdomains, Rev. Roum. Math. Pure Appl., XLIX, No. 3 (2004), 231-246 (with G. Groza)
92. A Galois theory for the Banach algebra of continuous symmetric functions on absolute Galois groups, Result. Math. 45, No. 3-4 (2004), 349-358. (with A. Popescu and A. Zaharescu)
93. On the continuity of the trace, Proceeding Romanian Academy, Series A, Volume 5, Number 2 (2004), 117-122. (with V. Alexandru and E. L Popescu)
94. Non-commutative valuation rings of the quotient artinian ring of a skew polynomial ring, Algebras and Representation Theory (2005), 8; 57-68 (with S. Kobayashi, H. Marubayashi, C. Vraciu and G. Xie)
95. A basis of C(X, Cp) over C(X, Qp), Rev. Roumaine Math. Pures Appl. Tome LI, Nr. 1 (2006), 87-88. (with E. L. Popescu)
96. On the structure of compact subsets of Cp, Acta Arithmetica, 123. 3 (2006), 253-266. (with A. D. R. Choudary, and A. Popescu)
97. On the existence of trace for elements of Cp, Algebras and Representation Theory (2006) 9: 47-66. (with M. Vajaitu and A. Zaharescu)
98. The p-adic measure on the orbit of an element of Cp, Rend. Sem. Mat. Univ. Padova, Vol.118 (2007), 197-216. (with V. Alexandru, M. Vajaitu and A. Zaharescu)
99. Analytic Normal Basis Theorem Cent. Eur. J. Math., 6 (3) (2008), 351-356. (with V. Alexandru and A. Zaharescu)
100. Norms on K[X1, . . . ,Xr], which are multiplicative on R, Result. Math., 51 (2008), 229-247. (with G. Groza and A. Zaharescu)
101. On the automorphisms of the spectral completion of the algebraic numbers field, Journal of Pure and Applied Algebra, 212 (2008), 1427–1431. (with E. L Popescu and A. Popescu)
102. All non–Archimedean norms on K[X1, . . . ,Xr], Glasg. Math. J. 52, (2010), No.1, 1-18 (with G. Groza and A. Zaharescu)
103. On the Iwasawa algebra associated to a normal element of Cp, Proc. Indian Acad. Sci. Math. Sci. 120, (2010), No. 1, 45-55. (with V. Alexandru, M. Vajaitu and A. Zaharescu)
104. A Galois Theory for the field extensions K((X))/ K, Glasg. Math. J. 52,(2010), 447-451 (with Asim Naseen and A. Popescu)
105. On the spectral norm of algebraic numbers (to appear in Math. Nachtr.) (with A. Popescu and A. Zaharescu)
106. The behavior of rigid analytic functions around orbits of elements of Cp (to appear) (with S. Achimescu, V. Alexandru, M. Vajaitu and A. Zaharescu)
107. On localizing systems in a Prüfer Domain (to appear in Communications in Algebra) (with H. Marubayashi and E.L. Popescu)
108. The study of the spectral p-adic extension (to appear in Proc. Rom. Acad.)
109. Some compact subsets of Qp (to appear in Rev. Roum. Math. Pures et Apll.)
110. Representation results for equivariant rigid analytic functions (to appear) (V. Alexandru, N. Popescu, M. Vajaitu and A. Zaharescu)
111. On the zeros of rigid analytic functions (to appear) (V. Alexandru, N. Popescu, M. Vajaitu and A. Zaharescu).
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and Emeritus Professor. Popescu was elected a Member of the Romanian Academy
Romanian Academy
The Romanian Academy is a cultural forum founded in Bucharest, Romania, in 1866. It covers the scientific, artistic and literary domains. The academy has 181 acting members who are elected for life....
in 1992. He is best known for his contributions to Algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
and the theory of Abelian categories. Since 1964 and until 2007 he collaborated on the characterization of abelian categories with the well-known French mathematician Pierre Gabriel. His areas of expertise were: Category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
, Abelian categories
Abelian category
In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototype example of an abelian category is the category of abelian groups, Ab. The theory originated in a tentative...
with Applications to Rings
Ring (mathematics)
In mathematics, a ring is an algebraic structure consisting of a set together with two binary operations usually called addition and multiplication, where the set is an abelian group under addition and a semigroup under multiplication such that multiplication distributes over addition...
and Modules
Module (mathematics)
In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring...
, adjoint functors, limits
Limit of a function
In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input....
/colimits,, Theory of Sheaves, Theory of Rings
Ring theory
In abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers...
, Fields
Field (mathematics)
In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...
and Polynomials, and Valuation Theory
Valuation (mathematics)
In algebra , a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field...
; he also has interests and published in the following areas: Algebraic Topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
, Algebraic Geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, Commutative Algebra
Commutative algebra
Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra...
, K-Theory
K-theory
In mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It...
, Class-Field theory
Class field theory
In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields.Most of the central results in this area were proved in the period between 1900 and 1950...
, and Algebraic Function Theory
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
. He published between 1962 and 2008 more than 102 papers in peer-reviewed, mathematics journals, several monographs on the theory of sheaves, and also six books on abelian category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
and abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
. In a Grothendieck-like, energetic style, he initiated and provided scientific leadership to several seminars on category theory, sheaves and abstract algebra which resulted in a continuous stream of high-quality mathematical publications in international, peer-reviewed mathematics journals by several members participating in his Seminar series. His book Abelian Categories with Applications to Rings and Modules continues to provide valuable information to mathematicians around the world. His latest contributions have also branched into valuation and number theory. He has published over 100 original, peer-reviewed articles in mathematics, mostly in category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
, algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, and Galois and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
.
Biography
Popescu was married, and there is a surviving wife Liliana and three children. He earned his M.S.Master of Science
A Master of Science is a postgraduate academic master's degree awarded by universities in many countries. The degree is typically studied for in the sciences including the social sciences.-Brazil, Argentina and Uruguay:...
degree in mathematics in 1964, and his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
degree in mathematics in 1967, both at the University of Bucharest
University of Bucharest
The University of Bucharest , in Romania, is a university founded in 1864 by decree of Prince Alexander John Cuza to convert the former Saint Sava Academy into the current University of Bucharest.-Presentation:...
. He was awarded a D. Phil. degree (Doctor Docent) in 1972 by the University of Bucharest.
In 2009 he carried out mathematics studies at the Institute of Mathematics of the Romanian Academy in the Algebra research group and also had international collaborations on three continents. One found from conversations with former Academician Nicolae Popescu that he shared many moral, ethical and religious values with another famous mathematician French-German-Jewish Alexander Grothendieck
Alexander Grothendieck
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
who visited the School of Mathematics in Bucharest in 1968. Like Grothendieck
he had a long-standing interest in category theory, number theory, practicing Yoga, and supporting promising young mathematicians in his fields of interest. He also supported the early developments of category theory applications in relational biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
and mathematical biophysics/mathematical biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
.
Academic positions
Popescu was appointed as a Lecturer at the University of Bucharest in 1968 where he taught graduate students until 1972. Since 1964, he also held a Research Professorship at the Institute of Mathematics of the Romanian AcademyInstitute of Mathematics of the Romanian Academy
The Institute of Mathematics "Simion Stoilow" of the Romanian Academy is a research institute in Bucharest, specialized in Mathematics. It was named after Simion Stoilow, who was its first Director, in 1949. In 1974 Nicolae Ceauşescu's daughter Zoia was permitted into the institute because of her...
, which institute was ruthlessly eliminated by former dictator and president of S.R. Romania, Nicolae Ceaușescu
Nicolae Ceausescu
Nicolae Ceaușescu was a Romanian Communist politician. He was General Secretary of the Romanian Communist Party from 1965 to 1989, and as such was the country's second and last Communist leader...
, in 1976 for reasons related to his daughter Zoe Ceaușescu who was 'hired' by the Mathematics Institute in Bucharest two years before.
Books published
- 1. Elemente de teoria algebrică a numerelor, Univ. București, 1968. (Elements of the Algebraic Theory of Numbers)
- 2. Teoria categoriilor și a fasciculelor, Ed. Stiintifica, 1971. (Category Theory and Sheaves)
- 3. Categorii Abeliene, Ed. Academiei, 1971. (Abelian Categories)
- 4 http://www.lib.iastate.edu:81/ipac20/ipac.jsp?session=1WB345344H890.711450&profile=parks&source=~!horizon&view=items&uri=full=3100001~!47305~!0&ri=1&aspect=basic_search&menu=search&ipp=20&spp=20&staffonly=&term=Modules+%28Algebra%29&index=PSUBJ&uindex=&aspect=basic_search&menu=search&ri=1#focusNicolae Popescu. Abelian categories with Applications to Rings and Modules, Academic Press, L. M. S. Monograph No.3, London, 1973, ISBN=0125615507.]
- 5. Popescu, Nicolae and Popescu, Liliana. Theory of categories. Martinus Nijhoff Publishers, The Hague; Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, 1979. x+337 pp. ISBN 90-286-0168-6.
- 6. Selected topics in Valuation Theory (to appear).
Original articles and references
1. Asupra omologiei si omotopiei C.W. - complexelor, Stud. Cerc. Mat., 1962 (On the singular homology of CW-complexes (with D. Burghelea)2. Diferențiale generalizate, Comunicările Acad. R.S.R., Tom 13, Nr. 6 (1963), 523-528. (with C. Bănică) (Generalized Differential Functions).
3. Quelques considérations sur l'exactitude des foncteurs, Bull. Math. Soc. Sci. Math. Phis. de la R. P. R. 7 (1963), 144-147. (with C. Bănică)
4. Modules à différentielle généralisée, Rev. Roumaine Math. Pures Appl. Tome IX, Nr. 6 (1964). 549-559.
5. Module cu diferentiala generalizata, Stud. Cerc. Mat. Tom 16, Nr. 6. (1964), 791-800.
6. La structure des modules injectifs sur an anneau á idéal principal, Bull. Math. de la Soc. Sci. Math. Phys. de la RPR Tome 8 (56), Nr. 1-2 (1964), 67-73. (with A. Radu)
7. Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C. R. Acad. Sci. Paris 258 (1964), 4188-4191. (with Pierre Gabriel)
8. Asupra categoriilor preabeliene (On pre-Abelian categories), Stud. Cerc. Mat. Tom 17 (1965), 563–575 (with C. Bănică)
9. Sur les catégories preabéliens, Rev. Roumaine Math. Pures Appl., 10(1965), 621-633. (with C. Bănică)
10. La localisation pour des sites, Rev. Roumaine Math. Pures Appl. 10 (1965), 1031-1044.
11. Categorii cat (Quotient categories), Stud. Cerc. Mat. Tom 17, Nr. 6 (1965), 951-985. (with C. Bănică)
12. Sur la structure des objets de certaines catégories abéliennes, C.R. Acad. Sci. Paris, t. 262(1966), 1295-1297. (with C. Năstăsescu)
13. Elemente de teoria fasciculelor I, (Elements of the theory of sheaves, I), Stud. Cerc. Mat. (1966) 267-296.
14. Elemente de teoria fasciculelor II (Elements of the theory of sheaves, I), Stud. Cerc. Mat. (1966) 407-456.
15. Elemente de teoria fasciculelor III (Elements of the theory of sheaves, III), Stud. Cerc. Mat. (1966) 547-583.
16. Elemente de teoria fasciculelor IV (Elements of the theory of sheaves, IV), Stud. Cerc. Mat. (1966) 647-669.
17. Morphismes et co-morphismes des topos abéliens, Bull. Math. de la Soc. Sci. Math. de la R.S.R. Tom 10 (58) Nr. 4 (1966), 319-328. (with A. Radu)
18. Elemente de teoria fasciculelor V (Elements of the theory of sheaves, V), Stud. Cerc. Mat. (1966) 945-991.
19. Quelques observations sur les topes abéliens, Rev. Roumaine Math. Pures Appl. 12 (1967), 553-563. (with C. Năstăsescu)
20. Théorie générale de la décomposition, Rev. Roum Math. Pures et Appl. Tome XII, Nr. 9 (1967), 1365-1371.
21. Elemente de teoria fasciculelor VI (Elements of the theory of sheaves, VI), Stud. Cerc. Mat. (1967) 205-240.
22. Anneaux semi-artiniens, Bull. Soc. Math. France 96 (1968), 357-368. (with C. Năstăsescu).
23. Sur les epimorphismes plats d'anneaux, C.R. Acad. Sci. Paris 268 (1969), 376-379. (with T. Spîrcu).
24. On the localization ring of ring, J. Algebra 15 (1970), 41-56. (with C. Năstăsescu)
25. Quelques observations sur les Épimorphismes plats (à Gauche) d’Anneaux, J. Algebra Vol. 16, Nr.1 (1970), 40-59. (with T. Spircu)
26. Sur les quasi-ordres (à gauche) dans un anneau, J. Algebra 17, Nr. 4 (1971), 474-481. (with D. Spulber)
27. Les anneaux semi-noethériens, C.R. Acad. Sci. Paris t. 272 (1971), 1439-1441.
28. Le spectre à gauche d'un anneau, J. Algebra 18, No. 2 (1971), 213-228.
29. Sur les C. P. anneaux, C.R. Acad. Sci. Paris t. 272 (1971), 1493-1496.
30. Théorie primaire de la décomposition dans les anneaux semi-noethériens, J. Algebra Vol. 23, No. 3 (1972), 482-492.
31. Quelques considérations sur les anneaux semi-artiniens commutatifs, C. R. Acad. Sci. Paris t. 276 (1973), 1545-1548.
32. Some remarks about semi-Artinian rings, Rev. Roumaine Math. Pures Appl. Tome XVIII, Nr. 9 (1973), 1413-1422. (with C. Vraciu)
33. Exemple de inele semi-artiniene, (Examples of semi-Artinian rings), Stud. Cerc. Math. Tom 26, Nr. 8 (1974), 1153-1157. (with T. Spîrcu)
34. Permanence Theorems for semi-artinian rings, Rev. Roumaine Math. Pures Appl. XXI, Nr.2 (1976), 227-231. (with T. Spircu)
35. Sur l'anneau des quotients d'un anneau noethérien (à droite) par rapport au système localisant associe à un idéal bilatéral premier, C.R. Acad. Sci. Paris.
36. Sur la structure des anneaux absolument plats commutatifs, J. Algebra Vol. 40, No. 2 (1976), 364-383. (with C. Vraciu)
37. Some remarks about the regular ring associated to a commutative ring, Rev. Roumaine Math. Pures et Appl. Tome XXIII (1978), 269-277. (with C. Vraciu)
38. Sur la sous-catégorie localisante associée à un idéal bilatéral premier dans un anneau noethérien (à droite), Rev. Roumaine Math. Pures Appl. Tome XXVI, Nr. 7 (1981), 1033-1042.
39. Sur un problème d'Arens et Kaplansky concernant la structure de quelques anneaux absolument plats commutatifs, Rev. Roumaine Math. Pures Appl., Tome. XXVII, Nr. 8 (1982), 867-874. (with C. Vraciu)
40. Sur une classe de polynômes irréductibles, C.R. Acad. Sci. Paris, t. 297 (1983), 9-11.
41. On a class of Prüfer domains, Rev. Roum. Math. Pures et Appl. Tome XXIX, Nr. 9 (1984), 777-786.
42. Galois Theory of permitted extensions of commutative regular rings, Bull. Math. Soc. Sci. Math. R.S. Roumanie, Tome 29 (77), nr. 2 (1985), 121-135. (with C. Vraciu)
43. On Dedekind Domains in Infinite Algebraic Extensions, Rend. Sem. Mat. Univ. Padova, Vol. 74 (1985), 39-44. (with C. Vraciu)
44. Local class field theory. I, (Romanian, Teoria locală a corpului claselor. I,. English summary), Stud. Cerc. Mat. 37 (1985), no. 4, 295–312.
45. On subfields of k(x), Red. Sem. Mat. Univ. Padova, Vol. 75 (1986), 257-273. (with V. Alexandru)
46. Local class field theory. II. (Romanian, Teoria locală a corpului claselor. I), Stud. Cerc. Mat. Tom 38, (1986), No.2, 107-138.
47. On a problem of Nagata in valuation theory, Rev. Roumaine Math. Pures Appl. Tome XXXI, Nr. 7 (1986), 639-641.
48. On a class of intermediate Subfields, Stud. Cerc. Mat., Tom 39, Nr. 2 (1987), p. 156-162. (with E.L. Popescu)
49. Sur une clase de prolongements à K(X) d'une valuation sur un corps K, Rev. Roumaine Math. Pures Appl., Tome XXXIII (1988), 393-400. (with V. Alexandru)
50. A theorem of characterization of residual transcendental extensions of a valuation, J. Math. Kyoto Univ. Vol. 28, Nr. 4 (1988), 579-592. (with V. Alexandru and A. Zaharescu)
51. Sur la définition des prolongements résiduels transcendents d'une valuation sur un corps K à K(X), Bull. Math. Soc. Sci. Math. Roumanie, Tome. 33 (1989), 257-264. (with E. L. Popescu)
52. Minimal pairs of definition of a residual transcendental extension of a valuation, J. Math. Kyoto, Univ., Vol. 30, Nr. 2 (1990), 207-225. (with V. Alexandru and A. Zaharescu)
53. All valuations on K(X), J. Math. Kyoto Univ., Vol. 30, Nr. 2 (1990), 281-296. (with V. Alexandru and A. Zaharescu)
54. On the residual transcendental extensions of a valuation. Key polynomials and augmented valuation, Math. Tsukuba Univ. Vol. 15, No.1 (1991), 57-78. (with E.L. Popescu)
55. A characterization of Generalized-Dedekind Domains, Bull. Math. de la Soc. Sci. Math. de Roumanie, Tome 35 (83), Nr.1-2 (1991), 139-141. (with E. L. Popescu)
56. On the Extension of Valuations on a Field K to K(X) – I, Red. Sem. Mat. Univ. Padova, Vol. 87 (1992), 151-168. (with C. Vraciu)
57. Some elementary remarks about n-local fields, Rend. Sem. Math. Univ. Padova, Vol. 91 (1994), 17-28 (with V. Alexandru)
58. On a class of valuations on K(X), 11th National Conference of Algebra, Constanta, 1994, An. St. Univ. Ovidius Constantza, Seria: Mat. Vol. II (1994), 120-136. [53] (with A. Zaharescu)
59. Sur une classe d'anneaux qui généralisent les anneaux de Dedekind, J. Algebra, Vol.173, (1995), 44-66. (with M. Fontana)
60. On the structure of the irreducible polynomials over local fields, J. Number Theory, Vol. 52, No. 1 (1995), 98-118. (with A. Zaharescu)
61. Sur une classe d’anneaux de Prüfer avec groupe de classes de torsion, Comm. Algebra 23 (1995), no. 12, 4521–4533. (with M. Fontana)
62. Completion of r. t. extension of a local field (I), Math. Z., Vol. 221 (1996), 675-682. (with V. Alexandru and A. Popescu)
63. On the extension of a valuation on a Field K to K(X) - II, Rend. Sem. Mat, Univ. Padova, Vol. 96 (1996), 1-14. (with C. Vraciu)
64. On a class of Domains having Prüfer integral closure: The FQR-domains, Commutative ring theory (Fès, 1995), 303-312, Lecture Notes in Pure and Appl. Math. Vol. 185, Dekker, New York, 1997. (with M. Fontana)
65. On the main invariant of an element over a local field, Portugalia Mathematica, Vol. 54, Fasc. 1 (1997), 73-83. (with A. Zaharescu)
66. On the closed subfields of Cp, J. Number Theory, Vol. 68, No. 2 (1998), 131-150. (with V. Alexandru and A. Zaharescu)
67. The Lüroth's Theorem for some complete fields, in Abelian Groups, Module Theory and Topology, Editors Dikranian-Salce, Marcel Dekker Inc., 1998, 55-58. (with V. Alexandru)
68. Abelian groups, module theory, and topology (Padua, 1997), 55–58, Lecture Notes in Pure and Appl. Math., 201, Dekker, New York, 1998.
69. Completion of r. t. extensions of local fields (II), Rend. Sem. Mat. Univ. Padova, Vol. 100 (1998). (with V. Alexandru and A. Popescu)
70. On the roots of a class of lifting polynomials, Fachbereich Math. Univ. Hagen, Band 63 (1998), 586-600. (with A. Zaharescu)
71. Invertible ideals and Picard group of generalized Dedekind domains, J. Pure and Appl. Alg., Vol 135, Nr. 3 (1999), 237-251. (with S. Gabelli)
72. The generating degree of Cp, Canad. Math. Bull. Vol. 44 (1), 2001, 3-11. (with V. Alexandru and A. Zaharescu)
73. Trace on Cp, J. Number Theory 88 (2001), Nr.1, 13-48. (with V. Alexandru and A. Zaharescu)
74. Spectral norms on valued fields, Math. Z., Vol. 238 (2001), 101-114. (with V. Pasol and A. Popescu)
75. Metric invariants in B+dR associated to differential operators, Rev. Roumaine Math. Pures Appl. XLVI, Nr. 5 (2001), 552-564. (with V. Alexandru and A. Zaharescu)
76. Completion of the Spectral extensions of p-adic valuation, Rev. Roum. Math. Pures et Apll, Vol. XLVI, Nr. 6 (2001), 805-817. (with E. L. Popescu and C. Vraciu)
77. Nagata Transform and Localizing Systems, Comm. in Algebra, 30(5), (2002), 2297-2308. (with Marco Fontana)
78. Chains of metric invariants over a local field, Acta Arithmetica, 103.1 (2002), 27-40. (with A. Popescu, M. Vajaitu and A. Zaharescu)
79. Universal property of the Kaplansky ideal transform and affineness of Open Subsets, J. Pure and Appl. Alg., 173, (2002), 121-134. (with Marco Fontana)
80. Total valuation rings of K(X, σ) containing K, Communications in Algebra, Volume 30, Number 11 (2002), 5535 – 5546. (with S. Kobayashi, H. Marubayashi and C. Vraciu)
81. On minimal pairs and residually transcendental extensions of valuations (Mathematika, 49 (2002), 93-106. (with S. Khanduja and K.W. Roggenkamp)
82. Total valuation rings of Ore extensions, Result. Math., 43 (2003), 373-379. (with S. Kobayashi, H. Marubayashi, C. Vraciu and G. Xie)
83. Galois action on plane compacts, Proceedings of the 35th Symposium on Ring Theory and Representation Theory (Okayama, 2002), 113–120, Symp. Ring Theory Represent Theory Organ. Comm., Okayama, 2003.
84. Transcendental divisors and their critical functions, Manuscripta Math., 110 (4), (2003), 527-541. (with A. Popescu and A. Zaharescu)
85. Trace Series on Q ̃K, Result. Math., 43 (2003), 331-341 (with A. Popescu and A. Zaharescu)
86. Metric invariants over Henselian valued Fields, J. Algebra, 266 (1), (2003), 14-26. (with A. Popescu and A. Zaharescu)
87. Galois structures on plane compacts, J. Algebra, 270, (2003), 238-248. (with A. Popescu and A. Zaharescu)
88. Good elements and metric invariants in B+dR, J. Math. Kyoto Univ, vol 43, Nr. 1 (2003), 125-137. (with V. Alexandru and A. Zaharescu)
89. A representation theorem for a class of rigid analytic functions, J. Th. Nombres Bordeaux, 15 (2003), 639-650. (with V. Alexandru and A. Zaharescu)
90. A characterization of completion of the spectral extension of p-adic valuation, World Conference on 21st Century Mathematics 2004, 157–161, Sch. Math. Sci.G.C. Univ., Lahore, 2004. (with E. L Popescu)
91. On afine subdomains, Rev. Roum. Math. Pure Appl., XLIX, No. 3 (2004), 231-246 (with G. Groza)
92. A Galois theory for the Banach algebra of continuous symmetric functions on absolute Galois groups, Result. Math. 45, No. 3-4 (2004), 349-358. (with A. Popescu and A. Zaharescu)
93. On the continuity of the trace, Proceeding Romanian Academy, Series A, Volume 5, Number 2 (2004), 117-122. (with V. Alexandru and E. L Popescu)
94. Non-commutative valuation rings of the quotient artinian ring of a skew polynomial ring, Algebras and Representation Theory (2005), 8; 57-68 (with S. Kobayashi, H. Marubayashi, C. Vraciu and G. Xie)
95. A basis of C(X, Cp) over C(X, Qp), Rev. Roumaine Math. Pures Appl. Tome LI, Nr. 1 (2006), 87-88. (with E. L. Popescu)
96. On the structure of compact subsets of Cp, Acta Arithmetica, 123. 3 (2006), 253-266. (with A. D. R. Choudary, and A. Popescu)
97. On the existence of trace for elements of Cp, Algebras and Representation Theory (2006) 9: 47-66. (with M. Vajaitu and A. Zaharescu)
98. The p-adic measure on the orbit of an element of Cp, Rend. Sem. Mat. Univ. Padova, Vol.118 (2007), 197-216. (with V. Alexandru, M. Vajaitu and A. Zaharescu)
99. Analytic Normal Basis Theorem Cent. Eur. J. Math., 6 (3) (2008), 351-356. (with V. Alexandru and A. Zaharescu)
100. Norms on K[X1, . . . ,Xr], which are multiplicative on R, Result. Math., 51 (2008), 229-247. (with G. Groza and A. Zaharescu)
101. On the automorphisms of the spectral completion of the algebraic numbers field, Journal of Pure and Applied Algebra, 212 (2008), 1427–1431. (with E. L Popescu and A. Popescu)
102. All non–Archimedean norms on K[X1, . . . ,Xr], Glasg. Math. J. 52, (2010), No.1, 1-18 (with G. Groza and A. Zaharescu)
103. On the Iwasawa algebra associated to a normal element of Cp, Proc. Indian Acad. Sci. Math. Sci. 120, (2010), No. 1, 45-55. (with V. Alexandru, M. Vajaitu and A. Zaharescu)
104. A Galois Theory for the field extensions K((X))/ K, Glasg. Math. J. 52,(2010), 447-451 (with Asim Naseen and A. Popescu)
105. On the spectral norm of algebraic numbers (to appear in Math. Nachtr.) (with A. Popescu and A. Zaharescu)
106. The behavior of rigid analytic functions around orbits of elements of Cp (to appear) (with S. Achimescu, V. Alexandru, M. Vajaitu and A. Zaharescu)
107. On localizing systems in a Prüfer Domain (to appear in Communications in Algebra) (with H. Marubayashi and E.L. Popescu)
108. The study of the spectral p-adic extension (to appear in Proc. Rom. Acad.)
109. Some compact subsets of Qp (to appear in Rev. Roum. Math. Pures et Apll.)
110. Representation results for equivariant rigid analytic functions (to appear) (V. Alexandru, N. Popescu, M. Vajaitu and A. Zaharescu)
111. On the zeros of rigid analytic functions (to appear) (V. Alexandru, N. Popescu, M. Vajaitu and A. Zaharescu).