Centralizing mappings of prime and semiprime *-rings

Abstract EN

In this paper we prove the following result.

Let R be a non-commutative prime *-ring of characteristic different from 2, then R is normal *- ring if and only if there exists a nonzero Jordan*- derivation d : R→R be which satisfies [d(x), x] ∈ Z (R) for all x ∈ R, and [d(h),s] ∈ Z (R) or [d (s), h] ∈ Z (R) for all h ∈ H (R), s ∈ S (R).