Some generalizations of semisimple gamma rings

Abstract EN

In this paper we introduce and study the concepts of semisimple gamma modules , regular gamma modules and fully idempotent gamma modules as a generalization of semisimple Γ-ring.

An R_Γ-module M is called fully R_Γ-idempotent (semisimple , regular) if N=(N:_(R_Γ ) M)ΓN for all R_Γ-submodule N of M (every R_Γ-submodule is a direct summand, for each m∈M, there exists fHom_(R_Γ ) (M,R) and γΓ such that m=f(m)γm.

We study some properties and relationships between them.