On commutativity of prime gamma rings with derivation

Authors : Okan ARSLAN, Hatice KANDAMAR

Pages : 1321-1328

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Publication Date : 2016-10-01

Article Type : Research Paper

Abstract :Let M be a weak Nobusawa Γ-ring and γ be a nonzero element of Γ. In this paper, we find a relation between Γ-rings and rings, and give some commutativity conditions on Γ-rings by using this relation. Also, we prove that any Γ-ring M in the sense of Nobusawa with a nonzero element γ in the center of M-ring Γ is γ-prime if and only if M is Γ-prime. As a consequence, we show that the semiprimeness insert ignore into journalissuearticles values(semisimpleness); of the ring insert ignore into journalissuearticles values(M, +, ·γ); for any γ ∈ Γ implies the Γsemiprimenessinsert ignore into journalissuearticles values(Γ-semisimpleness); of the Γ-ring M.
Keywords : gamma ring, prime Γ ring, k derivation, commutativity, γ radical