Bilinear maps on Artinian modules

Details Bilinear maps on Artinian modules Bilinear maps on Artinian modules

2011-08-11

arxiv.org/abs/1108.2520v1

Mathematics

Rings and Algebras

5 pages. Copy at http://math.berkeley.edu/~gbergman/papers may be updated more frequently than arXiv copy

Scientific paper

It is shown that if a bilinear map f: A x B --> C of modules over a commutative ring k is nondegenerate (i.e., if no nonzero element of A annihilates all of B, and vice versa), and A and B are Artinian, then A and B are of finite length. Some consequences are noted. Counterexamples are given to some attempts to generalize the above statement to balanced bilinear maps of bimodules over noncommutative rings, while the question is raised whether other such generalizations are true.

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