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

Nawaf Alsowait, Radwan M. Al-omary (), Zakia Al-Amery and Mohammed Al-Shomrani
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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

Mathematics, 2024, vol. 12, issue 15, 1-10

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.

Keywords: prime ideal; integral domain; ( ? , ? )-derivation; generalized ( ? , ? )-derivations; quotient ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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