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On a Quotient Ring That Satisfies Certain Identities via Generalized Reverse Derivations

Author

Listed:
  • Nawaf L. Alsowait

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

  • Mohammed Al-Shomrani

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

  • Radwan M. Al-omary

    (Department of Mathematics, Ibb University, Ibb 70270, Yemen)

  • Zakia Z. Al-Amery

    (Department of Mathematics, Aden University, Aden 5243, Yemen)

Abstract

In this article, for a prime ideal ρ of an arbitrary ring ℜ, we study the commutativity of the quotient ring ℜ / ρ , whenever ℜ admits a generalized reverse derivation ϑ associated with a reverse derivation ∂ that satisfies certain identities in ρ . Additionally, we show that, for some cases, the range of the generalized reverse derivation ϑ lies in the prime ideal ρ . Moreover, we explore several consequences and special cases. Throughout, we provide examples to demonstrate that various restrictions in the assumptions of our results are essential.

Suggested Citation

  • Nawaf L. Alsowait & Mohammed Al-Shomrani & Radwan M. Al-omary & Zakia Z. Al-Amery, 2025. "On a Quotient Ring That Satisfies Certain Identities via Generalized Reverse Derivations," Mathematics, MDPI, vol. 13(5), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:870-:d:1606101
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