Centrally Extended Jordan (*)-Derivations Centralizing Symmetric or Skew Elements

Let A be a non-commutative prime ring with involution *, of characteristic &NOTEQUexpressionL; 2 (and 3), with Z as the center of A and Pi a mapping Pi : A -> A such that [Pi(x), x] is an element of Z for all (skew) symmetric elements x is an element of A. If Pi is a non-zero CE-Jordan derivation of A, then A satisfies s(4), the standard polynomial of degree 4. If Pi is a non-zero CE-Jordan *-derivation of A, then A satisfies s4 or Pi(y) = lambda(y - y*) for all y is an element of A, and some lambda is an element of C, the extended centroid of A. Furthermore, we give an example to demonstrate the importance of the restrictions put on the assumptions of our results.