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Effects of Generalized Semiderivations on Algebraic Identities Involving Prime Ideals

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  • Kholood Alnefaie

Abstract

In this article, instead of a generalized derivation, we will use the concept of a generalized semiderivation ∇ that satisfies various identities involving a prime ideal ß of an optional ring Λ to describe the behavior of a quotient ring Λ/ß. We will use this concept to generalize some well‐known results that studied the behavior of a ring Λ via a generalized derivation. Additionally, we will list several consequences as well as some special cases as corollaries of our main theorems.

Suggested Citation

  • Kholood Alnefaie, 2025. "Effects of Generalized Semiderivations on Algebraic Identities Involving Prime Ideals," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:1318791
    DOI: 10.1155/jom/1318791
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    References listed on IDEAS

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    1. Nawaf Alsowait & Radwan M. Al-omary & Zakia Al-Amery & Mohammed Al-Shomrani, 2024. "Exploring Commutativity via Generalized ( α , β )-Derivations Involving Prime Ideals," Mathematics, MDPI, vol. 12(15), pages 1-10, July.
    2. Fuad Ali Ahmed Almahdi & Abdellah Mamouni & Mohammed Tamekkante, 2020. "A Generalization of Posner’s Theorem on Derivations in Rings," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 187-194, March.
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