Extensions of Simple Modules and the Converse of Schur's Lemma

Abstract

The converse of Schur's lemma (or CSL) condition on a module category has been the subject of considerable study in recent years. In this note we extend that work by developing basic properties of module categories in which the CSL condition governs modules of finite length.Comment: 8 pages, no figures, to appear, Proceedings of the International Conference on Algebra and its Applications, Ohio University, Athens, Ohio, June 18-21, 2008 (Birkh\"auser). Expository changes suggested by referee have been incorporate