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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
Also, we investigate some conditions on ideals of $\Gamma$-ring that make $M$ to be commutative.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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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Temel Bulgular & Veri:We also show that the common hypothesis\[a\alpha b\beta c=a\beta b\alpha c\: \text{for all}\: a,b,c\in M\:\text{and}\: \alpha,\beta\in\Gamma\]for a weak Nobusawa $\Gamma$-ring $M$ is sufficent for $M$ to be commutative.
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Sonuç & Katkı:Also, we investigate some conditions on ideals of $\Gamma$-ring that make $M$ to be commutative.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:prime ring · commutativity · prime $\Gamma$-ring
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 hypothesis\[a\alpha b\beta c=a\beta b\alpha c\: \text{for all}\: a,b,c\in M\:\text{and}\: \alpha,\beta\in\Gamma\]for a weak Nobusawa $\Gamma$-ring $M$ is sufficent for $M$ to be commutative. Also, we investigate some conditions on ideals of $\Gamma$-ring that make $M$ to be commutative.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
KANDAMAR, H., ARSLAN, O. (2020). On the commutativity conditions for rings and $\Gamma$-rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 5, 1660–1666. https://ajindex.com/articles/669265