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A Study of Generalized Differential Identities via Prime Ideals

Author

Listed:
  • Ali Yahya Hummdi
  • Kamal Charrabi
  • Shakir Ali
  • Abdellah Mamouni

Abstract

Let R be a ring and P be a prime ideal of R. The aim of this research paper is to delve into the relationship between the structural properties of the quotient ring R/P and the behavior of generalized derivations in a ring R endowed with an involution. Precisely, the study focuses on characterizing generalized derivations in the ring R that are associated with prime ideals and satisfy certain functional identities. The investigation seeks to uncover how these derivations interact with the quotient ring structure and the implications for the underlying ring theory. The key objective is to explore the relationship between a structure and a map, a topic that has proven to be highly significant. Moreover, we offer an example to show that the numerous conditions outlined in the hypotheses of our theorems are reasonable and not overly stringent.

Suggested Citation

  • Ali Yahya Hummdi & Kamal Charrabi & Shakir Ali & Abdellah Mamouni, 2025. "A Study of Generalized Differential Identities via Prime Ideals," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:7835503
    DOI: 10.1155/jom/7835503
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    References listed on IDEAS

    as
    1. Moulay Abdallah Idrissi & Lahcen Oukhtite, 2022. "Structure of a quotient ring $$\pmb {R/P}$$ R / P with generalized derivations acting on the prime ideal P and some applications," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(3), pages 792-800, September.
    2. Shakir Ali & Turki M. Alsuraiheed & Mohammad Salahuddin Khan & Cihat Abdioglu & Mohammed Ayedh & Naira N. Rafiquee, 2023. "Posner’s Theorem and ∗-Centralizing Derivations on Prime Ideals with Applications," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
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