Kernels of homomorphisms between uniform quasi-injective modules.

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? [ABSTRACT FROM AUTHOR]