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Some Generalizations of Semisimple Gamma Rings | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 58, Issue 3, 2018, Pages 1720-1728 | ||
| Authors | ||
| Emad Allawi Shallal; Saad Abdul kadhim Al-Saadi; Mehdi S. Abbas | ||
| 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 | ||
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