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is every finitely n-presented (S^{-1})R-module a localization of a finitely n-presented R-mo...

We can see that every finitely generated $(S^{-1})R$-module is a localization of a finitely generated R-module. … Then, more generally, is every finitely n-presented $ (S^{-1})R$-module a localization of a finitely n-presented R-module ? …