RESULTS ON alpha-*CENTRALIZERS OF PRIME AND SEMIPRIME RINGS WITH INVOLUTION

Abstract

Let R be a prime or semiprime ring equipped with an involution * and alpha be an automorphism of R. An additive mapping T : R -> R is called a left (resp. right) alpha(-)*centralizer of R if T (xy) = T (x)alpha (y*) (resp. T (xy) = alpha(x*)T (y)) holds for all x,y is an element of R, where a is an endomorphism of R. A left (resp. right) Jordan alpha-*centralizer T : R -> R is an additive mapping such that T (x(2)) = T (x)alpha(x*) (resp. T (x(2)) = alpha(x*)T (x)) holds for all x is an element of R. In this paper, we obtain some results about Jordan a-*centralizer of R with involution.