Lifting Ore sets of Noetherian filtered rings and applications (Q1911321)

If \(R\) is a filtered ring such that the Rees ring \(\widetilde{R}\) of \(R\) is left Noetherian, and \(T\) is a left Ore set of the associated graded ring \(G(R)\) consisting of homogeneous elements, then the saturated set \(S=\{s\in R,\;\sigma(s)\in T\}\) is a left Ore set of \(R\). The above lifting property is used to obtain local-global results on \(R\).