Results 21 to 30 of about 741 (55)
Effects of Generalized Semiderivations on Algebraic Identities Involving Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this article, instead of a generalized derivation, we will use the concept of a generalized semiderivation ∇ that satisfies various identities involving a prime ideal ß of an optional ring Λ to describe the behavior of a quotient ring Λ/ß. We will use this concept to generalize some well‐known results that studied the behavior of a ring Λ via a ...
Kholood Alnefaie, Pramita Mishra
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A Pair of Generalized (α, α)‐Derivations With Identities Related to Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let A be an arbitrary ring, α an automorphism of A, I a nonzero ideal of A, and ϒ a prime ideal of A satisfying the condition ϒ⊊αI. This research investigates the interplay between two generalized (α, α)‐derivations, Ω and G (associated with (α, α)‐derivations f and h, respectively), and the resulting characteristics of the quotient ring A/ϒ.
Ali Yahya Hummdi +4 more
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Coweakly Uniserial Modules and Rings Whose (2‐Generated) Modules Are Coweakly Uniserial
Journal of Mathematics, Volume 2025, Issue 1, 2025.A module is called weakly uniserial if for any two its submodules at least one of them is embedded in the other. This is a nontrivial generalization of uniserial modules and rings. Here, we introduce and study the dual of this concept. In fact, an R‐module M is called coweakly uniserial if for any submodules N, K of M, HomR(M/N, M/K) or HomR(M/K, M/N ...
M. M. Oladghobad +2 more
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A Unified Approach to Generalizing π‐Extending and π‐Baer Rings
Journal of Mathematics, Volume 2025, Issue 1, 2025.This paper introduces and examines the right essentially π‐Baer ring property, which serves as a new extension of the π‐extending and π‐Baer ring conditions. The initial phase of the study involves the development of several foundational results. The subsequent phase of the study involves the exploration of the transfer of the right essentially π‐Baer ...
Yeliz Kara, Ali Jaballah
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A Note on Skew Derivations and Antiautomorphisms of Prime Rings
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this article, we investigate the behavior of a prime ring which admits a skew derivation satisfying certain functional identities involving an antiautomorphism. We employ tools such as generalized identities and commutativity‐preserving maps to analyze these rings.
Faez A. Alqarni +5 more
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A Study of Generalized Differential Identities via Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let R be a ring and P be a prime ideal of R. The aim of this research paper is to delve into the relationship between the structural properties of the quotient ring R/P and the behavior of generalized derivations in a ring R endowed with an involution.
Ali Yahya Hummdi +4 more
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An Identity Related to Derivations of Standard Operator Algebras and Semisimple H*-Algebra¹
Cubo, 2010 In this paper we prove the following result. Let X be a real or complex Banach space, let L (X) be the algebra of all bounded linear operators on X, and let be a standard operator algebra. Suppose is a linear mapping satisfying the relation .
Irena Kosi-Ulbl, Joso Vukman
doaj
Endomorphism rings of modules over prime rings [PDF]
, 2012 Endomorphism rings of modules appear as the center of a ring, as the fix ring of ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain *-prime modules (introduced by Bican et al.) have a ...
Baziar, Mohammad, Lomp, Christian
core
Higher Derivations Satisfying Certain Identities in Rings
Journal of Mathematics, Volume 2024, Issue 1, 2024.Let n and m be fixed positive integers. In this paper, we establish some structural properties of prime rings equipped with higher derivations. Motivated by the works of Herstein and Bell‐Daif, we characterize rings with higher derivations D=dii∈N satisfying (i) dnx,dmy∈ZR for all x,y∈R and (ii) dnx,y∈ZR for all x,y∈R.
Amal S. Alali +4 more
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On Additivity and Multiplicativity of Centrally Extended (α, β)‐Higher Derivations in Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.In this paper, the concept of centrally extended (α, β)‐higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended (α, β)‐higher derivation is an (α, β)‐higher derivation.
O. H. Ezzat, Attila Gil nyi
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