Results 11 to 20 of about 97 (96)
On $*$-commuting mappings and derivations in rings with involution
TURKISH JOURNAL OF MATHEMATICS, 2016 Summary: Let \(R\) be a ring with involution \(*\). A mapping \(f:R\rightarrow R\) is said to be \(*\)-commuting on \(R\) if \([f(x),x^*]=0\) holds for all \(x\in R\). The purpose of this paper is to describe the structure of a pair of additive mappings that are \(*\)-commuting on a semiprime ring with involution.
Dar, Nadeem Ahmad, Ali, Shakir
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On derivations and commutativity of prime rings with involution
Georgian Mathematical Journal, 2015 Abstract In [Acta Math. Hungar. 66 (1995), 337–343], Bell and Daif proved that if R is a prime ring admitting a nonzero derivation such that d ( x
Ali, S., Dar, N.A., Aşçı, Mustafa
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2-Local derivations on associative and Jordan matrix rings over commutative rings
Linear Algebra and its Applications, 2017 The concept of 2-local derivations (resp. automorphisms) was introduced by \textit{P. Šemrl} [Proc. Amer. Math. Soc. 125, 2677--2680 (1997; Zbl 0887.47030)] who proved that every 2-local derivation (resp. automorphism) on \(B(H)\) is a derivation (resp. an automorphism), where \(H\) is an infinite-dimensional separable Hilbert space. In the paper under
Ayupov, Shavkat, Arzikulov, Farhodjon
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On derivations and commutativity in prime near-rings
Journal of Taibah University for Science, 2014 AbstractIn the present paper it is shown that zero symmetric prime right near-rings satisfying certain identities are commutative rings.
Ashraf, Mohammed +2 more
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Generalized reverse derivations and commutativity of prime rings [PDF]
Communications in Mathematics, 2019 Abstract Let R be a prime ring with center Z(R) and I a nonzero right ideal of R. Suppose that R admits a generalized reverse derivation (F, d) such that d(Z(R)) ≠ 0. In the present paper, we shall prove that if one of the following conditions holds: (i) F (xy) ± xy ∈ Z(R) (ii) F ([x, y]) ± [F (x), y] ∈ Z(R)
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On Ideals and Commutativity of Prime Rings with Generalized Derivations
European Journal of Pure and Applied Mathematics, 2018 An additive mapping F: R → R is called a generalized derivation on R if there exists a derivation d: R → R such that F(xy) = xF(y) + d(x)y holds for all x,y ∈ R. It is called a generalized (α,β)−derivation on R if there exists an (α,β)−derivation d: R → R such that the equation F(xy) = F(x)α(y)+β(x)d(y) holds for all x,y ∈ R. In the
Nawas, Mohammad Khalil Abu +1 more
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On b-generalized derivations and commutativity of prime rings
Revista Colombiana de MatemáticasLet A be a prime ring, Z(A) its center, Q its right Martindale quotient ring, C its extended centroid, ψ a non-zero b-generalized derivation of A with associated map ξ. In this article, we prove that: (i) If [ψ(x), ψ(y)] = 0 for all x, y ∈ A, then A is either commutative or there exists q ∈ Q such that ξ = ad(q), ψ(x) = -bxq, and qb = 0. (ii) If ψ(x) ◦
Alnoghashi, Hafedh M. +3 more
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On (m, n)-Jordan derivations and commutativity of prime rings
Demonstratio Mathematica, 2008 AbstractThe purpose of this paper is to prove the following result ...
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Derivations and commutativity of rings [PDF]
Pacific Journal of Mathematics, 1979 Chung, Lung O. +2 more
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Centralizing and Commuting Left Generalized Derivations on Prime Rings
Bulletin of Mathematical Sciences and Applications, 2015 Let R be a prime ring and d a derivation on R. If is a left generalized derivation on R such that ƒ is centralizing on a left ideal U of R, then R is commutative.
C. Jaya Subba Reddy +2 more
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