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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 40 Issue: 4

A Note on Generalized Left (t, p)-Derivations in Prime Rings

Xiao-wei Xu
Hong-ying Zhang
Pages
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Publication Date
2011-04-01
DOI
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⚡ TL;DR(Too Long; Didn't Read)

In this paper we describe generalized left (θ, φ)-derivations in prime rings, and prove that an additive mapping in a ring R acting as a homomorphism or anti-homomorphism on an additive subgroup S of R must be either a mapping acting as a homomorphism on S or a mapping acting as an anti-homomorphism on S, through which some related results are improved.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper we describe generalized left (θ, φ)-derivations in prime rings, and prove that an additive mapping in a ring R acting as a homomorphism or anti-homomorphism on an additive subgroup S of R must be either a mapping acting as a homomorphism on S or a mapping acting as an anti-homomorphism on S, through which some related results are improved.
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Key Findings & Data:In this paper we describe generalized left (θ, φ)-derivations in prime rings, and prove that an additive mapping in a ring R acting as a homomorphism or anti-homomorphism on an additive subgroup S of R must be either a mapping acting as a homomorphism on S or a mapping acting as an anti-homomorphism on S, through which some related results are improved.
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Conclusion & Impact:In this paper we describe generalized left (θ, φ)-derivations in prime rings, and prove that an additive mapping in a ring R acting as a homomorphism or anti-homomorphism on an additive subgroup S of R must be either a mapping acting as a homomorphism on S or a mapping acting as an anti-homomorphism on S, through which some related results are improved.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Prime rings · Generalized left (θ · Mappings acting as homomorphisms

Abstract

In this paper we describe generalized left (θ, φ)-derivations in prime rings, and prove that an additive mapping in a ring R acting as a homomorphism or anti-homomorphism on an additive subgroup S of R must be either a mapping acting as a homomorphism on S or a mapping acting as an anti-homomorphism on S, through which some related results are improved.

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Cite This Article

Xu, X., Zhang, H. (2011). A Note on Generalized Left (t, p)-Derivations in Prime Rings. Hacettepe Journal of Mathematics and Statistics, Volume: 40 Issue: 4. https://ajindex.com/articles/1403617

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