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On commutativity of prime gamma rings with derivation

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

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.

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

Abstract

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There are 2 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Okan Arslan This is me

Hatice Kandamar This is me

Publication Date October 1, 2016
Published in Issue Year 2016 Volume: 45 Issue: 5

Cite

APA Arslan, O., & Kandamar, H. (2016). On commutativity of prime gamma rings with derivation. Hacettepe Journal of Mathematics and Statistics, 45(5), 1321-1328.
AMA Arslan O, Kandamar H. On commutativity of prime gamma rings with derivation. Hacettepe Journal of Mathematics and Statistics. October 2016;45(5):1321-1328.
Chicago Arslan, Okan, and Hatice Kandamar. “On Commutativity of Prime Gamma Rings With Derivation”. Hacettepe Journal of Mathematics and Statistics 45, no. 5 (October 2016): 1321-28.
EndNote Arslan O, Kandamar H (October 1, 2016) On commutativity of prime gamma rings with derivation. Hacettepe Journal of Mathematics and Statistics 45 5 1321–1328.
IEEE O. Arslan and H. Kandamar, “On commutativity of prime gamma rings with derivation”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 5, pp. 1321–1328, 2016.
ISNAD Arslan, Okan - Kandamar, Hatice. “On Commutativity of Prime Gamma Rings With Derivation”. Hacettepe Journal of Mathematics and Statistics 45/5 (October 2016), 1321-1328.
JAMA Arslan O, Kandamar H. On commutativity of prime gamma rings with derivation. Hacettepe Journal of Mathematics and Statistics. 2016;45:1321–1328.
MLA Arslan, Okan and Hatice Kandamar. “On Commutativity of Prime Gamma Rings With Derivation”. Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 5, 2016, pp. 1321-8.
Vancouver Arslan O, Kandamar H. On commutativity of prime gamma rings with derivation. Hacettepe Journal of Mathematics and Statistics. 2016;45(5):1321-8.