Dedekind finite objects in module categories (Q1207522)

An object \(A\) of a category \({\mathcal C}\) is Dedekind finite if every \({\mathcal C}\)-monomorphism \(A\to A\) is a \({\mathcal C}\)-isomorphism (generalizing Dedekind's characterization of finite sets). This paper develops a series of results on Dedekind finite and co-Dedekind finite objects in the category of all unital left modules over a ring. The author relates these concepts to classical finiteness conditions on modules such as being finitely generated, ACC, DCC, etc., and characterizes the divisible Dedekind finite modules over a Dedekind domain.