A constructive proof of Orzech's theorem

Abstract

Let $A$ be a commutative ring with unity, and $M$ a finitely generated $A$-module. In 1971, Morris Orzech showed that any surjective $A$-module homomorphism from a submodule of $M$ to $M$ must be an isomorphism. We give a constructive proof of this fact using the Cayley--Hamilton theorem.

9 pages. Note written in 2015, mildly edited and with open questions added at the end. Posted mainly because I keep citing it. v2 fixes a mistake in the abstract and adds missing references