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

Let R be a prime or semiprime ring equipped with an involution * and α be an automorphism of R: An additive mapping T : R → R is called a left (resp. right) α-*centralizer of R if T (xy) = T (x) α (y*) (resp. T (xy) = α (x*) T (y)) holds for all x,y ∈ R; where α is an endomorphism of R. A left (resp. right) Jordan α-*centralizer T : R → R is an additive mapping such that T (x²) = T (x²) α(x*) (resp. T (x²) = α(x*)T (x)) holds for all x ∈ R: In this paper, we obtain some results about Jordan α-*centralizer of R with involution. [ABSTRACT FROM AUTHOR]