Bilinear maps on Artinian modules
Rings and Algebras
2013-05-10 v1
Abstract
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.
Cite
@article{arxiv.1108.2520,
title = {Bilinear maps on Artinian modules},
author = {George M. Bergman},
journal= {arXiv preprint arXiv:1108.2520},
year = {2013}
}
Comments
5 pages. Copy at http://math.berkeley.edu/~gbergman/papers may be updated more frequently than arXiv copy