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Journals / Turkish Journal of Mathematics / 2011 / Cilt: 35 - Sayı: 1

Generalized derivations on Lie ideals in prime rings

Öznur GÖLBAŞI
Emine KOÇ
Pages
23–28
Publication Date
2022-11-03
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d.
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Key Findings & Data:Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d.
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Conclusion & Impact:We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Derivations · Lie ideals · generalized derivations

Abstract

Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.

Özet

Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.

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Cite This Article

GÖLBAŞI, Ö., KOÇ, E. (2022). Generalized derivations on Lie ideals in prime rings. Turkish Journal of Mathematics, Cilt: 35 - Sayı: 1, 23–28. https://ajindex.com/articles/608469

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References (9)

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