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 f : A -> B, with A, B indecomposable (uniform) quasi-injective right R-modules, and g : E(A) -> E(B) an extension of f where E(-) denotes the injective hull, what is the relation between kernels of f and g, their monogeny classes and their upper parts?

Keywords

• Monogeny class
• semilocal ring
• direct-sum decompositions
• Krull-Schmidt theorem
• semilocal category
• preadditive category