Results 111 to 120 of about 6,477 (139)

On “On derivations and commutativity of prime rings with involution”

Georgian Mathematical Journal, 2020
Abstract In this note, we indicate some errors in [S. Ali, N. A. Dar and M. Asci, On derivations and commutativity of prime rings with involution, Georgian Math. J. 23 2016, 1, 9–14] and present the correct versions of the erroneous results.
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Commuting and centralizing generalized derivations on lie ideals in prime rings

Mathematical Notes, 2010
Let \(R\) be a noncommutative prime ring with \(\text{char\,}R\neq 2\), Utumi quotient ring \(U\), extended centroid \(C\), and noncentral Lie ideal \(L\). For \(x,y\in R\) set \([x,y]_1=xy-yx\) and for \(k\geq 1\) let \([x,y]_{k+1}=[[x,y]_k,y]_1\). The main result assumes that \(F\) and \(G\) are generalized derivations of \(R\) so that for a fixed ...
DE FILIPPIS, Vincenzo, F. Rania
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On n-commuting and n-skew-commuting maps with generalized derivations in prime and semiprime rings

Siberian Mathematical Journal, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
N. U. Rehman, DE FILIPPIS, Vincenzo
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Prime and Semiprime Rings with n-Commuting Generalized Skew Derivations

Bulletin of the Iranian Mathematical Society, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Derivations, products of derivations, and commutativity in near-rings

2019
For a zero-symmetric 3-prime near-ring N, we study three kinds of conditions: (a) conditions involving two derivations d(1), d(2) which imply that d(1) = 0 or d(2) = 0; (b) conditions involving derivations which force (N, +) to be abelian or N to be a commutative ring; (c) the condition that d(n)(S) is multiplicatively central for some derivation d and
Argac, N, Bell, HE
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Commutativity conditions on derivations and Lie ideals $��$-prime rings

2009
Let $R$ be a 2-torsion free $ $-prime ring, $U$ a nonzero square closed $ $-Lie ideal of $R$ and let $d$ be a derivation of $R$. In this paper it is shown that: 1) If $d$ is centralizing on $U$, then $d = 0$ or $U \subseteq Z(R)$. 2) If either $d([x, y]) = 0$ for all $x, y \in U$, or $[d(x), d(y)] = 0$ for all $x, y \in U$ and $d$ commutes with ...
Oukhtite, L., Salhi, S., Taoufiq, L.
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Commutativity and prime ideals in rings with involutions via derivations

Summary: This research explores the interplay between algebraic identities involving derivations with involutions and the commutativity of prime quotient rings. We aim to generalize established results that characterize commutativity in these rings.
Al-Omary, Radwan M., Rehman, Nadeem ur, Nisar, Junaid, Alnoghashi, Hafedh   +3 more
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A Generalization of Posner’s Theorem on Derivations in Rings

Indian Journal of Pure and Applied Mathematics, 2020
Fuad Ali Ahmed Almahdi, Abdellah Mamouni, Mohammed Tamekkante   +2 more
exaly  

Some commutativity theorems for prime rings with derivations and differentially semiprime rings

2016
Let \(R\) be a ring, \(U\) be a non-zero ideal of \(R\) and \(d\) be a derivation of \(R\). The results in this paper are of the type where commutativity relations involving images of elements of \(U\) under \(d\) are shown to be sufficient for \(R\) to be commutative. For example, Theorem 3 states that if \(R\) has no non-zero nilpotent \(d\)-ideal, \(
Hirano, Yasuyuki, Tominaga, Hisao
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Derivations of the intermediate Lie algebras between the Lie algebra of diagonal matrices and that of upper triangular matrices over a commutative ring

Linear and Multilinear Algebra, 2006
Shikun Ou
exaly