A new equation related to two-sided centralizers in prime rings.

In this paper we prove the following result: Let R be a prime ring with c h a r (R) ≠ 2 , 3 , 5 and let T : R → R be an additive mapping satisfying the relation T (x 4) = x T (x 2) x for all x ∈ R . In this case T is of the form T (x) = λ x for all x ∈ R and some fixed element λ ∈ C , where C is the extended centroid of R. [ABSTRACT FROM AUTHOR]