On bimodules over Noetherian PI rings

Abstract

Abstract. Let R be a prime Noetherian PI ring, and let I be an ideal in R satisfying xI ⊆ Ix for some x in R. We prove that xI = Ix. This is obtained as a corollary of a similar more general result, where I can be taken as any finitely generated torsion-free central R-bimodule.