On Ideals and Behavior of Quotient Rings via Generalized ( α, β )-Derivations

Nawaf L. Alsowait, Mohammed Al-Shomrani, Radwan M. Al-omary (), Zakia Z. Al-Amery and Hafedh Alnoghashi
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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
Hafedh Alnoghashi: Department of Basic Sciences, College of Engineering and IT, Amran University, Amran 9677, Yemen

Mathematics, 2025, vol. 13, issue 6, 1-14

Abstract: The purpose of this paper is to examine the behavior of a factor ring R / P with a partial range I of a ring R , where P is a prime ideal of R and I is a non-zero ideal of R such that P ⊊ I . In order to accomplish this objective, we will utilize specific algebraic identities that involve P and are related to generalized ( α , β ) -derivations F and G , associated with ( α , β ) -derivations d and g , respectively, where α and β are automorphisms of R . Additionally, we will list some important related consequences. Finally, we will provide an illustrative example to emphasize the importance of the hypotheses imposed in our theorems.

Keywords: prime ideal; integral domain; generalized ( α , β )-derivations; quotient ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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