Examples in noncommutative localization
Let R be a Noetherian ring and Q its Goldie localization at a prime ideal P. Using ideas from [\textit{L. W. Small} and \textit{J. T. Stafford}, J. Algebra 70, 156-161 (1981; Zbl 0478.16012)], the authors construct (i) an example of a ring R, finitely generated as a module over its Noetherian centre, for which the localization Q at a maximal ideal is neither left nor right Noetherian and (ii) an example where Q is Noetherian on one side only.
scientific article; zbMATH DE number 3950749