Results 21 to 30 of about 104 (51)
Derivatives of triangular, Toeplitz, circulant matrices and matrices of other forms over semirings [PDF]
, 2017 In this article we construct examples of derivations in matrix semirings. We study hereditary and inner derivations, derivatives of diagonal, triangular, Toeplitz, circulant matrices and of matrices of other forms and prove theorems for derivatives of matrices of these forms.
arxiv +1 more source
Derivations of higher order in semiprime rings
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 89-92, 1998., 1997 Let R be a 2‐torsion free semiprime ring with derivation d. Supposed d2n is a derivation of R, where n is a positive integer. It is shown that if R is (4n − 2)‐torsion free or if R is an inner derivation of R, then d2n−1 = 0.
Jiang Luh, Youpei Ye
wiley +1 more source
Action of prime ideals on generalized derivations-I [PDF]
arXiv, 2021 In the present paper, we investigate the commutativity of quotient ring $R/P$ where $R$ is any ring and $P$ is a prime ideal of $R$ which admits generalized derivations are satisfying some algebraic identities acting on prime ideals $P$.
arxiv
Commutativity results for semiprime rings with derivations
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 471-474, 1998., 1996 We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [d(x), d(y)] = 0 for all x, y ∈ R, to the case of semiprime rings. An extension of this result is proved for a two‐sided ideal but is shown to be not true for a one‐sided ideal.
Mohammad Nagy Daif
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 263-266, 1997., 1995 Let R be a ring A bi‐additive symmetric mapping d : R × R → R is called a symmetric bi‐derivation if, for any fixed y ∈ R, the mapping x → D(x, y) is a derivation. The purpose of this paper is to prove the following conjecture of Vukman. Let R be a noncommutative prime ring with suitable characteristic restrictions, and let D : R × R → R and f : x → D ...
Qing Deng
wiley +1 more source
Commuting Jordan derivations on triangular rings are zero [PDF]
arXiv, 2023 The main purpose of this article is to show that every commuting Jordan derivation on triangular rings (unital or not) is identically zero. Using this result, we prove that if $\mathcal{A}$ is a 2-torsion free ring such that it is either semiprime or satisfies Condition (P), then every commuting Jordan derivation from $\mathcal{A}$ into itself, under ...
arxiv
A note on semiprime rings with derivation
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 413-415, 1997., 1996 Let R be a 2‐torsion free semiprime ring, I a nonzero ideal of R, Z the center of R and D : R → R a derivation. If d[x, y] + [x, y] ∈ Z or d[x, y] − [x, y] ∈ Z for all x, y ∈ I, then R is commutative.
Motoshi Hongan
wiley +1 more source
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
wiley +1 more source
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
S‐J‐Ideals: A Study in Commutative and Noncommutative Rings
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this paper, we introduce the concept of S‐J‐ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that many properties of J‐ideals apply to S‐J‐ideals and examine their characteristics in various ring constructions, such as homomorphic image rings, quotient rings, cartesian ...
Alaa Abouhalaka +3 more
wiley +1 more source