On certain classes of modules (Q2366865)

Given a class of modules which is closed under isomorphism and contains the zero module, the author studies the closure properties of certain related classes. One of the concepts used is that of dual Goldie dimension. This material is applied to give characterisations of Artinian modules, and in particular to give the following dual to the reviewer's characterisation of left Noetherian rings: If \(R\) is a semi-perfect ring then \(R\) is left Artinian if and only if every left ideal of \(R\) is the direct sum of an injective left ideal and an Artinian left ideal.