Linear systems over localizations of rings

摘要

We describe a method for solving linear systems over the localization of a commutative ring R at a multiplicatively closed subset S that works under the following hypotheses: the ring R is coherent, i.e., we can compute finite generating sets of row syzygies of matrices over R, and there is an algorithm that decides for any given finitely generated ideal the existence of an element r in and in the affirmative case computes r as a concrete linear combination of the generators of I.