Generalized ( τ, σ )- L -Derivations in Rings

Hicham Saber, Zakia Z. Al-Amery, Radwan M. Al-omary, Khaled Aldwoah (), Amer Alsulami and Muntasir Suhail ()
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Hicham Saber: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
Zakia Z. Al-Amery: Department of Mathematics, Aden University, Aden 5243, Yemen
Radwan M. Al-omary: Department of Mathematics, Ibb University, Ibb 70270, Yemen
Khaled Aldwoah: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
Amer Alsulami: Department of Mathematics, Turabah University College, Taif University, Taif 21944, Saudi Arabia
Muntasir Suhail: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Mathematics, 2025, vol. 13, issue 17, 1-17

Abstract: Let τ and σ : X ⟶ X be automorphisms of an arbitrary associative ring X , and let L be a prime ideal of X . The main objective of this article is to combine the notions of generalized L -derivations and ( τ , σ ) - L -derivations by introducing and analyzing a novel additive mapping Π : X → X called a generalized ( τ , σ ) - L -derivation associated with a ( τ , σ ) - L -derivation π . Later, we will examine the algebraic properties of a factor ring X / L under the influence of certain algebraic expressions containing this generalized ( τ , σ ) - L -derivation and lying in a prime ideal L . Through our main findings, we establish certain results under different conditions. It also provides various illustrative examples to show that our primeness hypotheses in various theorems are not exaggerated.

Keywords: ( τ , σ )-ℙ-derivation; generalized ( τ , σ )-ℙ-derivation; integral domain; prime ideal; commutativity; mathematical operators; factor ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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