Results 11 to 20 of about 59,526 (169)
On Centrally Semiprime Rings and Centrally Semiprime [PDF]
Kirkuk Journal of Science, 2008 In this paper, two new algebraic structures are introduced which we call a centrally semiprime ring and a centrally semiprime right near-ring, and we look for those conditions which make centrally semiprime rings as commutative rings, so that several ...
Adil Kadir Jabbar +1 more
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Commutativity with Derivations of Semiprime Rings
Discussiones Mathematicae - General Algebra and Applications, 2020 Let R be a 2-torsion free semiprime ring with the centre Z(R), U be a non-zero ideal and d: R → R be a derivation mapping.
Atteya Mehsin Jabel
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The $X$-semiprimeness of Rings [PDF]
arXivFor a nonempty subset $X$ of a ring $R$, the ring $R$ is called $X$-semiprime if, given $a\in R$, $aXa=0$ implies $a=0$. This provides a proper class of semiprime rings. First, we clarify the relationship between idempotent semiprime and unit-semiprime rings.
Grigore Călugăreanu +2 more
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On the Structure of Semiprime Rings [PDF]
Proceedings of the American Mathematical Society, 1973 The structure of prime rings has recently been studied by A. W. Goldie, R. E. Johnson, L. Lesieur and R. Croisot. In their main results some sort of finiteness assumption is invariably made. It is shown in this paper that certain semiprime rings are subdirect sums of full rings of linear transformations of a right vector space over a division ring.
Augusto H. Ortiz
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Remarks on derivations on semiprime rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 1992 We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy+d(xy)=yx+d(yx) for all x, y in R, or (ii) xy−d(xy)=yx−d(yx) for all x, y in R.
Mohamad Nagy Daif, Howard E. Bell
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Regular elements in semiprime rings [PDF]
Proceedings of the American Mathematical Society, 1968 In the proof of Goldie's theorem [1, Theorem 4.1], one of the crucial steps is to establish that every large right ideal contains a regular element [1, Theorem 3.9]. Recently, S. A. Amitsur told one of the authors he had proved, using the weaker conditions of the ACC on left and right annihilators, that every prime ring contains a left regular element ...
R. E. Johnson, Lawrence S. Levy
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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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