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Keywords = generalized (τ, σ)-ℙ-derivation

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17 pages, 327 KB  
Article
Generalized (τ, σ)-L-Derivations in Rings
by Hicham Saber, Zakia Z. Al-Amery, Radwan M. Al-omary, Khaled Aldwoah, Amer Alsulami and Muntasir Suhail
Mathematics 2025, 13(17), 2784; https://doi.org/10.3390/math13172784 - 29 Aug 2025
Cited by 1 | Viewed by 1096
Abstract
Let τ and σ:XX 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 [...] Read more.
Let τ and σ:XX 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:XX 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. Full article
(This article belongs to the Section A: Algebra and Logic)
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