Differential identities with automorphisms and antiautomorphisms, I

Abstract

AbstractLet R be a prime associative ring with the extended centroid C. Assume that R satisfies a nontrivial differential identity with automorphisms and antiautomorphisms. It is shown here that R must satisfy a nontrivial ordinary generalized polynomial identity (without derivations, automorphisms, and antiautomorphisms). When this is combined with Martindale's result on generalized polynomial identities, it follows that the central closure RC of R is a primitive ring with nonzero socle and its skew field is finite dimensional over C