Results 21 to 30 of about 1,149,018 (192)
On centralizers of semiprime rings [PDF]
Aequationes Mathematicae, 2003 The main result of this paper is the following. Let R be a 2-torsion free semiprime ring and let $ T : R \rightarrow R $ be an additive mapping such that $ 2T(xyx) = T(x)yx + xyT(x) $ holds for all $ x,y \in R $. Then T is a centralizer.
Joso Vukman, Irena Kosi-Ulbl
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DERIVATIONS OF PRIME AND SEMIPRIME RINGS [PDF]
Journal of the Korean Mathematical Society, 2009 Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+yd(x)) n = xy + yx for all x,y 2 I, then R is commutative. (ii) If charR 6 2 and (d(x)y + xd(y) + d(y)x + yd(x)) n i (xy + yx) is central for all x,y 2 I, then R is commutative.
Nurcan Argaç, Hülya İnceboz
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Journal of Applied Mathematics and Computational Mechanics, 2014 In this paper we present some results for FDI-rings, i.e. rings with a complete set of pairwise orthogonal primitive idempotents. We consider the nilpotency index of ideals and give its upper band for ideals in some classes of rings. We also give a new proof of a criterion of semiprime FDI-rings to be prime.
Nadiya Gubareni
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A note on semiprime rings with derivation [PDF]
International Journal of Mathematics and Mathematical Sciences, 1997 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
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On Semiprime Rings of Bounded Index [PDF]
Proceedings of the American Mathematical Society, 1982 A ring R R is of bounded index (of nilpotency) if there is an integer n ⩾ 1 n \geqslant 1 such that x n = 0 {x^n} = 0 whenever x ∈ R x \in R is nilpotent. The least
Efraim P. Armendariz
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Dependent Elements of Derivations on Semiprime Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 We characterize dependent elements of a commuting derivation d on a semiprime ring R and investigate a decomposition of R using dependent elements of d.
Faisal Ali, Muhammad Anwar Chaudhry
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Additive mappings satisfying algebraic identities in semiprime rings [PDF]
Discussiones Mathematicae - General Algebra and Applications, 2023 Abu Zaid Ansari
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On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings
Journal of new theory, 2022 The algebraic properties and identities of a semiprime ring are investigated with the help of the multiplicative (generalised)-(α, α)-reverse derivation on the non-empty ideal of the semiprime ring.
Handan Karahan +2 more
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Open Mathematics, 2022 Generalized Munn rings exist extensively in the theory of rings. The aim of this note is to answer when a generalized Munn ring is primitive (semiprimitive, semiprime and prime, respectively).
Guo Junying, Guo Xiaojiang
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