Helmut Ulm
Encyclopedia
Helmut Ulm was a German
mathematician
who established the classification of countable
periodic
abelian group
s by means of their Ulm invariants.
. After finishing high school in Wuppertal
in 1926, he attended the universities of Göttingen (1926–1927), Jena (1927) and Bonn
(1927–1930), where he studied mathematics and physics, attending the lectures of Richard Courant
, Erich Bessel-Hagen, Felix Hausdorff
, and the joint Hausdorff–Otto Toeplitz
seminar. He graduated summa cum laude in 1930 with a thesis about countable periodic abelian groups (1933). In 1933–1935 he was an assistant in Göttingen and worked with Wilhelm Magnus
and Olga Taussky-Todd editing David Hilbert
's Collected Works. His Habilitationschrift developed a generalization of the elementary divisor theory to infinite matrices, continuing ideas of Ulm's teacher Toeplitz.
It was submitted in Münster in 1936 and refereed by Heinrich Behnke
, Gottfried Köthe
, F. K. Schmidt, and B. L. van der Waerden. Ulm's promotion was delayed, apparently, due to his anti-Nazi views.
From 1935 until his retirement in 1974 Ulm worked at the University of Münster
, as an assistant, docent, and eventually professor (1968). Besides his three important papers on the classification of infinite abelian groups, Ulm published only a few notes in the proceedings of the Münster mathematical seminar, one of which dealt with solution of systems of linear equations by a computer. He suffered from poor health. During the World War II
, Ulm worked as a cryptographer. After the war he mostly taught courses in applied mathematics and supervised several Ph.D. theses; those of G. Tillmann (1952) and G. Roth (1961) were close to his old work on infinite-dimensional linear algebra and infinite groups.
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
mathematician
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....
who established the classification of countable
Countable set
In mathematics, a countable set is a set with the same cardinality as some subset of the set of natural numbers. A set that is not countable is called uncountable. The term was originated by Georg Cantor...
periodic
Periodic group
In group theory, a periodic group or a torsion group is a group in which each element has finite order. All finite groups are periodic. The concept of a periodic group should not be confused with that of a cyclic group, although all finite cyclic groups are periodic.The exponent of a periodic group...
abelian group
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order . Abelian groups generalize the arithmetic of addition of integers...
s by means of their Ulm invariants.
Short biography
Helmut Ulm's father was an elementary school teacher in ElberfeldElberfeld
Elberfeld is a municipal subdivision of the German city of Wuppertal; it was an independent town until 1929.-History:The first official mentioning of the geographic area on the banks of today's Wupper River as "elverfelde" was in a document of 1161...
. After finishing high school in Wuppertal
Wuppertal
Wuppertal is a city in North Rhine-Westphalia, Germany. It is located in and around the Wupper river valley, and is situated east of the city of Düsseldorf and south of the Ruhr area. With a population of approximately 350,000, it is the largest city in the Bergisches Land...
in 1926, he attended the universities of Göttingen (1926–1927), Jena (1927) and Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
(1927–1930), where he studied mathematics and physics, attending the lectures of Richard Courant
Richard Courant
Richard Courant was a German American mathematician.- Life :Courant was born in Lublinitz in the German Empire's Prussian Province of Silesia. During his youth, his parents had to move quite often, to Glatz, Breslau, and in 1905 to Berlin. He stayed in Breslau and entered the university there...
, Erich Bessel-Hagen, Felix Hausdorff
Felix Hausdorff
Felix Hausdorff was a Jewish German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis.-Life:Hausdorff studied at the University of Leipzig,...
, and the joint Hausdorff–Otto Toeplitz
Otto Toeplitz
Otto Toeplitz was a German Jewish mathematician working in functional analysis.- Life and work :...
seminar. He graduated summa cum laude in 1930 with a thesis about countable periodic abelian groups (1933). In 1933–1935 he was an assistant in Göttingen and worked with Wilhelm Magnus
Wilhelm Magnus
Wilhelm Magnus was a mathematician. He made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations....
and Olga Taussky-Todd editing David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
's Collected Works. His Habilitationschrift developed a generalization of the elementary divisor theory to infinite matrices, continuing ideas of Ulm's teacher Toeplitz.
It was submitted in Münster in 1936 and refereed by Heinrich Behnke
Heinrich Behnke
Heinrich Behnke was a German mathematician and rector at the University of Münster.- Life and career :...
, Gottfried Köthe
Gottfried Köthe
Gottfried Maria Hugo Köthe was an Austrian mathematician working in abstract algebra and functional analysis.- Scientific career :...
, F. K. Schmidt, and B. L. van der Waerden. Ulm's promotion was delayed, apparently, due to his anti-Nazi views.
From 1935 until his retirement in 1974 Ulm worked at the University of Münster
University of Münster
The University of Münster is a public university located in the city of Münster, North Rhine-Westphalia in Germany. The WWU is part of the Deutsche Forschungsgemeinschaft, a society of Germany's leading research universities...
, as an assistant, docent, and eventually professor (1968). Besides his three important papers on the classification of infinite abelian groups, Ulm published only a few notes in the proceedings of the Münster mathematical seminar, one of which dealt with solution of systems of linear equations by a computer. He suffered from poor health. During the World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, Ulm worked as a cryptographer. After the war he mostly taught courses in applied mathematics and supervised several Ph.D. theses; those of G. Tillmann (1952) and G. Roth (1961) were close to his old work on infinite-dimensional linear algebra and infinite groups.