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On $ \theta$-centralizers of semiprime rings (II)

Author(s): M. N. Daif; M. S. Tammam El-Sayiad
Original publication: Algebra i Analiz, tom 21 (2009), nomer 1.
Journal: St. Petersburg Math. J. 21 (2010), 43-52.
MSC (2000): Primary 16N60
Posted: November 4, 2009
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Abstract: The following result is proved: Let $ R$ be a 2-torsion free semiprime ring, and let $ T : R \to R$ be an additive mapping, related to a surjective homomorphism $ \theta : R\to R$, such that $ 2T(x^2)=T(x)\theta(x)+\theta(x) T(x)$ for all $ x\in R$. Then $ T$ is both a left and a right $ \theta$-centralizer.

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Additional Information:

M. N. Daif
Affiliation: Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
Email: nagydaif@yahoo.com

M. S. Tammam El-Sayiad
Affiliation: Department of Mathematics, Faculty of Science, Beni Suef University, Beni Suef, Egypt
Email: m_s_tammam@yahoo.com

DOI: 10.1090/S1061-0022-09-01084-X
PII: S 1061-0022(09)01084-X
Keywords: Prime ring, semiprime ring, left(right) centralizer, left(right) $\theta $-centralizer, left(right) Jordan $\theta $-centralizer, derivation, Jordan derivation
Received by editor(s): 28/SEP/2007
Posted: November 4, 2009
Copyright of article: Copyright 2009, American Mathematical Society

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