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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Also, we investigate some conditions on ideals of Γ-ring that make M to be commutative.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper we observe the relation between the center of R-ring R and the center of usual ring R and then prove if the center of R-ring R is nonzero, then R is commutative as a ring.
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Key Findings & Data:We also show that the common hypothesisaαbβc = aβbαc for all a, b, c ∈ M and α, β ∈ Γfor a weak Nobusawa Γ-ring M is sufficent for M to be commutative.
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Conclusion & Impact:Also, we investigate some conditions on ideals of Γ-ring that make M to be commutative.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let R be any ring. In this paper we observe the relation between the center of R-ring R and the center of usual ring R and then prove if the center of R-ring R is nonzero, then R is commutative as a ring. We also show that the common hypothesisaαbβc = aβbαc for all a, b, c ∈ M and α, β ∈ Γfor a weak Nobusawa Γ-ring M is sufficent for M to be commutative. Also, we investigate some conditions on ideals of Γ-ring that make M to be commutative.
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Cite This Article
KANDAMAR, H., ARSLAN, O. (2022). On the commutativity conditions for rings and Γ-rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 5, 1660–1666. https://ajindex.com/articles/529638