On commutativity of prime gamma rings with derivation

Year 2016, Volume: 45 Issue: 5, 1321 - 1328, 01.10.2016

Okan Arslan Hatice Kandamar

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 (semisimpleness) of the ring (M, +, ·γ) for any γ ∈ Γ implies the Γsemiprimeness(Γ-semisimpleness) of the Γ-ring M.

Keywords

gamma ring, prime Γ-ring, k-derivation, commutativity, γ-radical

References

• .
• .