Jordan ?-Centralizers of Prime and Semiprime Rings

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Abdulrahman H. Majeed
Mushreq I. Meften

Abstract

The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: R?R an additive mapping such that T is left (right) Jordan ?-centralizers on R. Then T is a left (right) ?-centralizer of R, if one of the following conditions hold (i) R is a semiprime ring has a commutator which is not a zero divisor . (ii) R is a non commutative prime ring . (iii) R is a commutative semiprime ring, where ? be surjective endomorphism of R . It is also proved that if T(x?y)=T(x)??(y)=?(x)?T(y) for all x, y ? R and ?-centralizers of R coincide under same condition and ?(Z(R)) = Z(R) .

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How to Cite
1.
Jordan ?-Centralizers of Prime and Semiprime Rings. Baghdad Sci.J [Internet]. 2010 Dec. 5 [cited 2024 Mar. 28];7(4):1426-31. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/1121
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How to Cite

1.
Jordan ?-Centralizers of Prime and Semiprime Rings. Baghdad Sci.J [Internet]. 2010 Dec. 5 [cited 2024 Mar. 28];7(4):1426-31. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/1121

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