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.
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