Unimodular form
Encyclopedia
In mathematics
, in the module theory of a commutative ring
, a bilinear form on a module
V is unimodular if it induces an isomorphism
.
Here
denotes the dual module of V.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, in the module theory of a commutative ring
Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra....
, a bilinear form on a module
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...
V is unimodular if it induces an isomorphism
.Here
denotes the dual module of V.