Kernels of homomorphisms between uniform quasi-injective modules

Abstract

In this paper, we study the behavior of endomorphism rings of indecomposable (uniform) quasi-injective modules. A very natural question here is, for a morphism [Formula: see text], with [Formula: see text] indecomposable (uniform) quasi-injective right [Formula: see text]-modules, and [Formula: see text] an extension of [Formula: see text] where [Formula: see text] denotes the injective hull, what is the relation between kernels of [Formula: see text] and [Formula: see text], their monogeny classes and their upper parts?