Direct Sum of E- Injective N-Groups

Abstract

Extending the notion of relative injectivity of modules to near-ring groups, we define E-injective near-ring groups and characterize such near-ring groups. The nature of E-injective N-groups under direct sum is studied in this paper. The notion of dominance of an element of an N-group by another N-group plays an important role in establishing the fact that the direct sum of a family of E-injective N-groups is also E-injective. If near-ring group E satisfies chain conditions on its substructures, then inheritance of E-injective character of direct sum of E-injective N-groups is also established.