On Jordan*- Centralizers On Gamma Rings With Involution

  • Rajaa C .Shaheen Department of Mathematics, College of Education, University of Al-Qadisiya, Al-Qadisiya, Iraq.
Keywords: -ring,involution, prime -ring,semi-prime -ring , left centralizer, Left* centralizer ,Right centralizer, Right* centralizer, centralizer, Jordan *centralizer.

Abstract

    Let M be a 2-torsion free-ring with involution satisfies the condition xyz=xyz for all x,y,zM and ,.an additive mapping *: M→Mis called Involution if and only if (ab)*=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(aa)=T(a)a* (resp., T(aa)=a* T(a ))holds for all aM,.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 . 

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Published
2017-09-16
How to Cite
C .Shaheen, R. (2017). On Jordan*- Centralizers On Gamma Rings With Involution. Journal of Al-Qadisiyah for Computer Science and Mathematics, 3(1), 52-58. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/239
Section
Math Articles