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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
We also study the additive maps $d : M\rightarrow M$ such that $d(u\alpha u)=2u\alpha d(u)$, where $u\in U$ and $\alpha\in\Gamma$, and show that $d(u\alpha v)=u\alpha d(v) + v\alpha d(u)$, for all $u,v\in U$ and $\alpha\in\Gamma$.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let $M$ be a $2$-torsion free $\sigma$-prime $\Gamma$-ring and $U$ be a non-zero $\sigma$-square closed Lie ideal of $M$.
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Temel Bulgular & Veri:If $T :M\rightarrow$ $M$ is an automorphism on $U$ such that $T\ne 1$ and $T\sigma =\sigma T$ on $U$, then we prove that $U\subseteq Z(M)$.
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Sonuç & Katkı:We also study the additive maps $d : M\rightarrow M$ such that $d(u\alpha u)=2u\alpha d(u)$, where $u\in U$ and $\alpha\in\Gamma$, and show that $d(u\alpha v)=u\alpha d(v) + v\alpha d(u)$, for all $u,v\in U$ and $\alpha\in\Gamma$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$\sigma$-prime $\Gamma$-ring · centralizing automorphisms · Lie ideals
Abstract
Let $M$ be a $2$-torsion free $\sigma$-prime $\Gamma$-ring and $U$ be a non-zero $\sigma$-square closed Lie ideal of $M$. If $T :M\rightarrow$ $M$ is an automorphism on $U$ such that $T\ne 1$ and $T\sigma =\sigma T$ on $U$, then we prove that $U\subseteq Z(M)$. We also study the additive maps $d : M\rightarrow M$ such that $d(u\alpha u)=2u\alpha d(u)$, where $u\in U$ and $\alpha\in\Gamma$, and show that $d(u\alpha v)=u\alpha d(v) + v\alpha d(u)$, for all $u,v\in U$ and $\alpha\in\Gamma$.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
DEY, K. K., PAUL, A. C., DAVVAZ, B. (2022). On centralizing automorphisms and Jordan left derivations on $\sigma$-prime gamma rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 1, 51–57. https://ajindex.com/articles/529113