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A note on a pair of derivations of semiprime rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 We study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f, g be derivations of R such that f(x)x+xg(x)∈Z(R) for all x∈R, then f and g are ...
Muhammad Anwar Chaudhry, A. B. Thaheem
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AN IDENTITY RELATED TO θ-CENTRALIZERS IN SEMIPRIME RINGS [PDF]
Journal of Algebraic Systems, 2023 Let $R$ be a $ 2$-torsion-free semiprime ring and $\theta$ be an epimorphism of $R$. In this paper, under special hypotheses, we prove that if $T: R\longrightarrow R$ is an additive mapping such that$$T(xyx)=θ(x)T(y)θ(x),$$holds for
Abbas Zivari-Kazempour
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A note on Jordan left *-centralizers on prime and semiprime rings with involution
Journal of Taibah University for Science, 2017 The aim of this note is to give alternative and short proofs for some results to Ali et al. in [3] by using the relationship between the concepts of Jordan left *-centralizer and right centralizer on a 2-torsion free semiprime rings endowed with ...
M.S. Tammam El-Sayiad +2 more
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Mathematica BohemicaWe study McCoy's theorem to the skew Hurwitz series ring $({\rm HR}, \omega)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings.
Rajendra Kumar Sharma, Amit B. Singh
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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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Notes on Semiprime Ideals with Symmetric Bi-Derivation
AxiomsIn this paper, we prove many algebraic identities that include symmetric bi-derivation in rings which contain a semiprime ideal. We intend to generalize previous results obtained for semiprime rings with symmetric derivation using semiprime ideals in ...
Ali Yahya Hummdi +3 more
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International Journal of Mathematics and Mathematical Sciences, 2000 For prime rings R, we characterize the set U∩CR([U,U]), where U is a right ideal of R; and we apply our result to obtain a commutativity-or-finiteness theorem. We include extensions to semiprime rings.
Howard E. Bell
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ON JORDAN IDEAL IN PRIME AND SEMIPRIME INVERSE SEMIRINGS WITH CENTRALIZER
Al-Mustansiriyah Journal of Science, 2020 In this paper we recall the definition of centralizer on inverse semiring. Also introduce the definition of Jordan ideal and Lie ideal. Some results of M.A.Joso Vukman on centralizers on semiprime rings are generalized here to inverse semirings.
Rawnaq Khaleel Ibraheem +1 more
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On Generalized Left Derivation on Semiprime Rings [PDF]
Engineering and Technology Journal, 2016 Let R be a 2-torsion free semiprime ring. If R admits a generalizedleft derivation F associated with Jordan left derivation d, then R is commutative, if any one of the following conditions hold: (1) [d(x), F(y)] [x, y], (2) [d(x), F(y)] xoy, (3) d(x ...
A. Majeed, Shaima,a Yass, a B. Yass
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Identities on additive mappings in semiprime rings
Математичні Студії, 2023 Consider a ring $R$, which is semiprime and also having $k$-torsion freeness. If $F, d : R\to R$ are two additive maps fulfilling the algebraic identity $$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$ for each $x$ in $R.$ Then $F$ will be a generalized derivation ...
A. Z. Ansari, N. Rehman
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