Linear systems over localizations of rings

Abstract

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 $I\subseteq R$ the existence of an element $r$ in $S\cap I$ and in the affirmative case computes $r$ as a concrete linear combination of the generators of $I$.

Improvement of the method

References in corpus (1)

• An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization

Cited by in corpus (3)

• An algorithmic approach to Chevalley's Theorem on images of rational morphisms between affine varieties
• A constructive approach to Freyd categories
• Constructive Arithmetics in Ore Localizations Enjoying Enough Commutativity