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ON CENTRALIZERS ON SOME GAMMA RING | ||
| journal of al-qadisiyah for pure science(quarterly) | ||
| Article 1, Volume 7, Issue 2, 2007, Pages 219-229 PDF (0 K) | ||
| Author | ||
| Rajaa C .Shaheen | ||
| Abstract | ||
| Let M be a 2-torsion free -ring satisfies the condition x y z=x y z for all x,y,zM and , . In section one ,we prove if M be a completely prime -ring and T:M→M an additive mapping such that T(a a)=T(a) a (resp., T(a a)=a T(a ))holds for all aM, .Then T is a left centralizer or M is commutative (res.,a right centralizer or M is commutative) and so every Jordan centralizer on completely prime -ring M is a centralizer .In section two ,we prove this problem but by another way. In section three we prove that every Jordan left centralizer(resp., every Jordan right centralizer) on -ring has a commutator right non-zero divisor(resp., on -ring has a commutator left non-zero divisor)is a left centralizer(resp., is a right centralizer) and so we prove that every Jordan centralizer on -ring has a commutator non –zero divisor is a centralizer . | ||
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