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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2019 / Cilt: 9 Sayı: 1

Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings

Asal ve Yarıasal Halkalarda Ters ve Jordan (𝜶,𝜷)−bitürev

Barış ALBAYRAK
Neşet AYDIN
Pages
149–164
Publication Date
2019-06-28
DOI
—
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AI Summary & Key Takeaways

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

In addition, we investigate commutative feature of prime ring with Jordan left α- biderivation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we prove that any nonzero reverse (α,β)- biderivation on a prime ring is (α,β)- biderivation.
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Key Findings & Data:Also, we show that any Jordan (α,β)- biderivation on non-commutative semi-prime ring R with char(R)≠2 is an (α,β)- biderivation.
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Conclusion & Impact:In addition, we investigate commutative feature of prime ring with Jordan left α- biderivation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Asal halka · Yarı-asal halka · prime ring

Abstract

In this study, we prove that any nonzero reverse (α,β)- biderivation on a prime ring is (α,β)- biderivation. Also, we show that any Jordan (α,β)- biderivation on non-commutative semi-prime ring R with char(R)≠2 is an (α,β)- biderivation. In addition, we investigate commutative feature of prime ring with Jordan left α- biderivation.

Özet

Bu çalışmada, asal halka üzerinde tanımlı sıfırdan farklı bir ters (𝛼,𝛽)− bitürevin aynı zamanda (𝛼,𝛽)− bitürev olduğu ispatlanmıştır. Ayrıca, 𝑐ℎ𝑎𝑟(𝑅)≠2 olacak biçimdeki değişmeli olmayan bir yarı-asal 𝑅 halkası üzerinde tanımlı Jordan (𝛼,𝛽)− bitürevin aynı zamanda (𝛼,𝛽)− bitürev olduğu gösterilmiştir. Bunların yanında, Jordan sol (𝛼,𝛼)−bitürevli asal halkaların değişmeli olma özellikleri araştırılmıştır.

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Cite This Article

ALBAYRAK, B., AYDIN, N. (2019). Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 9 Sayı: 1, 149–164. https://ajindex.com/articles/920486

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References (1)

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