Derivations in Gamma Rings with γ-Lie and γ-Jordan Structures

Abstract

Let M be weak Nobusawa Γ-ring and γ be non-zero element of Γ. In this paper, we study the definition of γ-semi prime Γ-ring, and introduce definition of γ-semi simple Γ-ring and γ-Jordan ideal of M. We give equivalent definitions for γ-prime Γ-ring and γ-semi prime Γ-ring. Also by using relation between Γ-rings and rings, we give some commutativity conditions on Γ-rings.