In this paper we have proved the following results. (1) If $d(U)subset Z$ then $U subset Z$ (2) If $d(U)subset U$ and $d^2(U)subset Z$ then $Usubset Z$.
📌 3 Key Takeaways
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Objective & Hypothesis:Let R be a prime ring, char $Rneq 2,3 sigma, tau : R rightarrow R$ two automorphisms, U a nonzero ($sigma$, $tau$)- Lie ideal of R and $oneq d : R rightarrow R$ a derivation such that $sigma d = d sigma, tau d = d tau$.
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Key Findings & Data:Let R be a prime ring, char $Rneq 2,3 sigma, tau : R rightarrow R$ two automorphisms, U a nonzero ($sigma$, $tau$)- Lie ideal of R and $oneq d : R rightarrow R$ a derivation such that $sigma d = d sigma, tau d = d tau$.
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Conclusion & Impact:In this paper we have proved the following results. (1) If $d(U)subset Z$ then $U subset Z$ (2) If $d(U)subset U$ and $d^2(U)subset Z$ then $Usubset Z$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let R be a prime ring, char $Rneq 2,3 sigma, tau : R rightarrow R$ two automorphisms, U a nonzero ($sigma$, $tau$)- Lie ideal of R and $oneq d : R rightarrow R$ a derivation such that $sigma d = d sigma, tau d = d tau$. In this paper we have proved the following results. (1) If $d(U)subset Z$ then $U subset Z$ (2) If $d(U)subset U$ and $d^2(U)subset Z$ then $Usubset Z$.
Özet
Bu makalede aşağıdaki sonuçlar ispatlanmıştır. R, char $Rneq 2,3$ olan bir asal halka ,U,R nin sıfırdan farklı bir ideali, $sigma$ ve $tau$ R nin iki otomorfizmi ve $oneq d : R rightarrow R,dsigma=d sigma, tau d=dtau$ olacak şekilde R nin bir türevi olsun 1)Z,R nin merkezi olmak üzere $d(U)subset Z$ ise $U subset Z$ (2) If $d(U)subset U$ ve $d^2(U)subset Z$ ise $Usubset Z$ dir.
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Cite This Article
SOYTÜRK, M. (2022). Türevli asal halkalarda ($sigma$, $tau$) -Lie idealler. Turkish Journal of Mathematics, Cilt: 20 - Sayı: 2, 233–236. https://ajindex.com/articles/609011