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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]

Let R be a *-prime ring with characteristic different from two and U ≠ 0 be a square closed *-Lie ideal of R. An additive mapping F : R → R is called an generalized derivation if there exits a derivation d : R → R such that F(xy) = F(x)y+xd(y). In the present paper, it is shown that U ⊆ Z if R is a *-prime ring which admits a generalized derivation satisfying several conditions that are associated with a derivation commuting with *. [ABSTRACT FROM AUTHOR]

In this paper, we extend the results concerning generalized derivations of prime rings in [2] and [8] for a nonzero Lie ideal of a prime ring R. [ABSTRACT FROM AUTHOR]