Bilinear maps on Artinian modules

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.

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

References in corpus (1)

• Homomorphisms on infinite direct product algebras, especially Lie algebras