On bimodules over Noetherian PI rings

Abstract

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