Results 41 to 50 of about 68 (65)
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
wiley +1 more source
Generalized (; )-derivations and Left Ideals in Prime and Semiprime Rings
, 2017 Let R be an associative ring, ; be the automorphisms of R, be a nonzero left ideal of R, F : R ! R be a generalized (; )-derivation and d : R ! Rbe an (; )-derivation.
Rahaman, Hamidur, Ali, Asma
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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
wiley +1 more source
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
wiley +1 more source
A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this paper, we introduce the concept of weakly semiprime ideals and weakly n‐systems in noncommutative rings. We establish the equivalence between an ideal P being a weakly semiprime ideal and R − P being a weakly n‐system. We provide alternative definitions and explore the properties of weakly semiprime ideals.
Alaa Abouhalaka, Francesca Tartarone
wiley +1 more source
IDENTITIES WITH DERIVATIONS AND AUTOMORPHISMS ON SEMIPRIME RINGS
, 2020 The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative ...
Joso Vukman
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Ad-nilpotent elements in algebras and superalgebras
, 2021 Tesis Doctoral leída en la Universidad Rey Juan Carlos de Madrid en 2021. Directores de la Tesis: Esther García González y Miguel Ángel Gómez LozanoIn this thesis we will deal with ad nil potent elements in associative algebras and super algebras with ...
Vera de Salas, Guillermo
core
Jordan superderivations and superhomomorphisms and functional identities
, 2015 O objetivo desta dissertação é apresentar a generalização de alguns resultados, válidos para anéis, para o contexto de superálgebras. Em 1957, I. N. Herstein provou que toda derivação de Jordan em um anel primo de característica diferente de 2 é uma ...
Willian Ribeiro Valencia da Silva +1 more
core +1 more source
A sheaf representation for non-commutative rings /
, 1987 For any ring R (associative with 1) we associate a space X of prime torsion theories endowed with Golan's SBO-topology. A separated presheaf L(-,M) on X is then constructed for any right R-module M$ sb{ rm R}$, and a sufficient condition on M is given ...
Rumbos, Irma Beatriz
core
On a Functional Identity Involving Power Values of Generalized Skew Derivations on Lie Ideals
Let R be a prime ring, Qr its right Martindale quotient ring and C its extended centroid. Suppose that F is a generalized skew derivation of R, L a non-central Lie ideal of R, m,n,s≥1 positive fixed integers.
Carini Luisa, De Filippis Vincenzo
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