QUASI-INJECTIVE NEAR-RING GROUPS

Abstract

We extend the concepts of quasi-injective modules and their en- domorphism rings to near-ring groups. We attempt to derive the near-ring character of the set of endomorphism of quasi-injective N-groups under certain conditions and this leads us to a near-ring group structure which motivates us to study various characteristics of the structure. If E is a quasi-injective N-group and S = End(injective hull of E) then we study the structure ES and various properties of ES. It is proved that ES is a minimal quasi-injective exten- sion of E and any two minimal quasi-injective extensions are equivalent. This structure motivates to study the Jacobson radical of endomorphism near-ring of quasi-injective N-group E. It is established that the near-ring modulo the Jacobson radical is a regular near-ring. Some properties of quasi-injective N- groups relating essentially closed N-subgroups and complement N-subgroups are established.