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Exploring Commutativity via Generalized ( α , β )-Derivations Involving Prime Ideals

Author

Listed:
  • Nawaf Alsowait

    (Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia)

  • Radwan M. Al-omary

    (Department of Mathematics, Ibb University, Ibb, Yemen)

  • Zakia Al-Amery

    (Department of Mathematics, Aden University, Aden, Yemen)

  • Mohammed Al-Shomrani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

The purpose of this article is to enhance the previous studies regarding the behavior of a quotient ring ℑ / ℘ , where ℘ is a prime ideal in a ring ℑ . In particular, we are going to explore more general scenarios whenever a ring ℑ admits a generalized ( α , β ) -derivation associated with an ( α , β ) -derivation ∂ that satisfies certain criteria involving ℘ , where α and β are automorphisms on ℑ . Moreover, we provide some examples to demonstrate the importance of the assumptions made in our results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2325-:d:1442391
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