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ON JORDAN*- CENTRALIZERS ON GAMMA RINGS WITH INVOLUTION | ||
| Journal of Al-Qadisiyah for Computer Science and Mathematics | ||
| Article 1, Volume 3, Issue 1, 2011, Pages 1-6 PDF (0 K) | ||
| Author | ||
| Rajaa C .Shaheen | ||
| Abstract | ||
| Let M be a 2-torsion free -ring with involution satisfies the condition x y z=x y z for all x,y,z M and , .an additive mapping *: M→Mis called Involution if and only if (a b)*=b* a*and (a*)*=a . In section one of this paper ,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 a M, .Then T is an anti- left *centralizer or M is commutative (res.,an anti- right* centralizer or M is commutative) and so every Jordan* centralizer on completely prime -ring M is an anti- *centralizer or M is commutative. In section two 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 an anti- left *centralizer(resp., is an anti- right *centralizer) and so we prove that every Jordan* centralizer on -ring has a commutator non –zero divisor is an anti-* centralizer . | ||
| Keywords | ||
| ring; involution; Prime; semi; left centralizer; left; Right centralizer; right; centralizer; Jordan | ||
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