Singular and semi-simple character in E-injective N-groups with weakly descending chain conditions

Abstract

Injective modules and near-ring groups have been studied by several researchers like Mason et al., Faith et al., Jara, Harada, Cheng. Of these Oswald and Mason have studied injective and projective near-ring modules. Mason studied injective near-ring modules and defined the concepts like n-injective, loosely injective and almost injective near-ring modules. In Hazarika and Saikia (Int J Math Sci 33(2), 2013) we extended the notion of relative injectivity of modules to near-ring groups. Here E-injective N-groups with descending chain conditions are studied. It is shown that the singular and semi-simple characters play a vital role in characterization of E-injective N-groups with weakly descending chain conditions.