Quadratic central polynomials with derivation and involution

Abstract

The main result of this paper shows that if R is a prime ring with involution and with derivation D, then if p (x, y) = c 1 xy D +c 2 x D y+c 3 yx D +c 4 y D x is central for all (skew-) symmetric elements of R, then R must embed in M 2 (F), with two explicit exceptions. As a consequence of the special case when x = y, one obtains generalizations of existing results about (skew-) centralizing derivations of the (skew-) symmetric elements