The Module Isomorphism Problem for Finite Rings and Related Results

Abstract

Let $R$ be a finite ring and let $M,N$ be two finite left $R$-modules. We present two distinct deterministic algorithms that decide in polynomial time whether or not $M$ and $N$ are isomorphic, and if they are, exhibit an isomorphism. As by-products, we are able to determine the largest isomorphic common direct summand between two modules and the minimum number of generators of a module. By not requiring $R$ to contain a field, avoiding computation of the Jacobson radical and not distinguishing between large and small characteristic, both algorithms constitute improvements to known results.

arXiv comment7 pages, submitted, an abstract of this paper appeared in ACM Communications in Computer Algebra, Volume 49, Issue 1, page 14, March 2015