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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 2

Generalized derivations centralizing on Jordan ideals of rings with involution

Lahcen OUKHTITE
Abdellah MAMOUNI
Pages
225–232
Publication Date
2014-05-16
DOI
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AI Summary & Key Takeaways

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

Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative.
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Key Findings & Data:In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results.
💡
Conclusion & Impact:Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Rings with involution · generalized derivations · Jordan ideals

Abstract

A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

Özet

A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

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Cite This Article

OUKHTITE, L., MAMOUNI, A. (2014). Generalized derivations centralizing on Jordan ideals of rings with involution. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 2, 225–232. https://ajindex.com/articles/185713

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References (13)

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