Quadratic central polynomials with derivation and involution

Charles Philip Lanski

Vol. 155 (1992), No. 1, 111–127

DOI: 10.2140/pjm.1992.155.111

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) = c₁xy^D + c₂x^Dy + c₃yx^D + c₄y^Dx is central for all (skew-) symmetric elements of R, then R must embed in M₂(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.

Mathematical Subject Classification 2000

Primary: 16R50

Secondary: 16N60

Milestones

Received: 11 June 1990

Revised: 17 June 1991

Published: 1 September 1992