On Modules over a Serial Ring Whose Endomorphism Rings are Quasi-Frobenius

Introduction The purpose of this paper is to establish several necessary and sufficient conditions for a module over a serial ring to have a quasiFrobenius endomorphism ring. In the study of properties of modules, it is greatly important to investigate their endomorphism rings. By Schur’s Lemma the endomorphism ring of a simple module is a division ring, and we have enough knowledge about the endomorphism rings of modules over a semi-simple ring. Here we shall investigate the following problem: PROBLEM. Find a necessary and sufficient condition for a module