Title of article :
Some Generalizations of Semisimple Gamma Rings
Author/Authors :
abbas, mehdi s. al-mustansiriyah university - college of science - department of mathematics, Iraq , al-saadi, saad abdul kadhim al-mustansiriyah university - college of science - department of mathematics, Iraq , shallal, emad allawi al-mustansiriyah university - college of science - department of mathematics, Iraq
Abstract :
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 f∈〖Hom〗_(R_Γ ) (M,R) and γ∈Γ such that m=f(m)γm. We study some properties and relationships between them
Keywords :
Semisimple Gamma Module , Multiplication Gamma Module , Duo Gamma Module , Fully Idempotent Gamma Module , Regular Gamma Module
Journal title :
Iraqi Journal Of Science
Journal title :
Iraqi Journal Of Science
