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