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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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.
📌 3 Key Takeaways
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Objective & Hypothesis:Let M be a weak Nobusawa Γ-ring and γ be a nonzero element of Γ.
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Key Findings & Data:In this paper, we find a relation between Γ-rings and rings, and give some commutativity conditions on Γ-rings by using this relation.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:gamma ring · prime Γ-ring · k-derivation
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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Cite This Article
Arslan, O., Kandamar, H. (2016). On commutativity of prime gamma rings with derivation. Hacettepe Journal of Mathematics and Statistics, Volume: 45 Issue: 5. https://ajindex.com/articles/1403090