Jordan Gamma*-centralizers and reverse Gamma*-centralizers on semiprime Gamma-ring with involution

摘要

Let M be a semiprime ..-ring with involution. An additive mappingT : M ! M is called left(right) Jordan .. -Centralizer if T(x x) =T(x) x (x T(x)) for all x 2 M and 2 ... If T is both left and rightJordan .. -centralizer of M, then T is called a Jordan .. -centralizer.The subsetZ(M) = fx 2 M; x m = m x; for all m 2 M and 2 ..giscalled the center of the ..-ring M. In this paper, it is shown that anadditive mapping T on a 2-torsion free semiprime ..-ring with involutionsatis es 2T(x x) = T(x) x + x T(x) for all x 2 M and 2 .., thenT is a reverse .. -centralizer.