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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In the present paper it is shown that if $d^2(U)=(0)$, then $U\subset Z$.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $R$ be a $\ast$-prime ring with characteristic not 2, $U$ be a nonzero $\ast$-$(\sigma,\tau)$-Lie ideal of $R$ and $d$ be a nonzero derivation of $R$.
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Key Findings & Data:Suppose $\sigma$, $\tau$ be two automorphisms of $R$ such that $\sigma d=d\sigma$, $\tau d=d\tau$ and $\ast$ commutes with $\sigma,\tau,d$.
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Conclusion & Impact:In the present paper it is shown that if $d^2(U)=(0)$, then $U\subset Z$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Derivations · $(\sigma · \tau)$-Lie Ideals
Abstract
Let $R$ be a $\ast$-prime ring with characteristic not 2, $U$ be a nonzero $\ast$-$(\sigma,\tau)$-Lie ideal of $R$ and $d$ be a nonzero derivation of $R$. Suppose $\sigma$, $\tau$ be two automorphisms of $R$ such that $\sigma d=d\sigma$, $\tau d=d\tau$ and $\ast$ commutes with $\sigma,\tau,d$. In the present paper it is shown that if $d^2(U)=(0)$, then $U\subset Z$.
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Cite This Article
AYDIN, N., KOÇ, E., GÖLBAŞI, Ö. (2018). On $\ast$-$(\sigma,\tau)$-Lie ideals of $\ast$-prime rings with derivation. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 5, 1240–1247. https://ajindex.com/articles/669428