Archiv der Mathematik

, Volume 111, Issue 1, pp 23–32 | Cite as

Linear systems over localizations of rings

  • Sebastian PosurEmail author


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.


Computable ring Coherent strongly discrete ring Linear system Localization 

Mathematics Subject Classification

Primary 13B30 Secondary 13P20 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SiegenSiegenGermany

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