Kernel–Injective Module

Abstract

In this work, the notion of injectivity relative to a class of closed kernel sub modules (namely, kernel-injectivity) has been introduced and studied, which is a generalization quasi-injective module. This notion is closed under direct summands. Several properties and characterizations have been given.we provide a characterization of semi simple Artinian ring , SI-ring and Dedekind domain in terms of Ker-quasi-injective R-module