On Hermitian endomorphism rings

Abstract

Let [Formula: see text] be a right [Formula: see text]-module with finite exchange property and let [Formula: see text] be its endomorphism ring. In this paper, some sufficient and necessary conditions for [Formula: see text] to be a Hermitian ring are given. Moreover, we investigate Hermitian endomorphism rings of quasi-projective modules by means of completions of diagrams. The dual problems for quasi-injective modules are also studied.