Ore extensions of Jacobson rings

Abstract

It is shown that, under suitable conditions, an Ore extension R[. x ; α] of a Jacobson ring R (i.e., a ring all of whose prime ideals are semiprimitive) with a monomorphism α, will be Jacobson. These conditions are satisfied by the class of rings studied by Pearson, Stephenson and Watters, and by left Noetherian rings, giving a theorem of Goldie and Michler. © 2014 Elsevier Inc.