On Goldie prime ideals of ore extensions

Abstract

Let R be a ring and α an injective endomorphism of R, which is not assumed to be surjective. Necessary and sufficient conditions are given for all prime ideals in a skew polynomial ring R[x; α] or skew Laurent ring R[x, x-1; α] to be left Goldie. As a consequence, we obtain a generalization of a result of Goldie and Michler. © Taylor & Francis Group, LLC.