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Jordan -Centralizers of Prime and Semiprime Rings | ||
| Baghdad Science Journal | ||
| Article 1, Volume 7, Issue 4, 2010, Pages 1426-1431 | ||
| Authors | ||
| Mushreq I. Meften; Abdulrahman H. Majeed | ||
| Abstract | ||
| The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: RR 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(xy)=T(x)(y)=(x)T(y) for all x, y R and -centralizers of R coincide under same condition and (Z(R)) = Z(R) . | ||
| Keywords | ||
| prime ring; semiprime ring; left; centralizer; Jordan centralizer; Jordan | ||
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