The Module Isomorphism Problem for Finite Rings and Related Results
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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.
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