Papers › Computing Gröbner Bases and Free Resolutions of OI-Modules
Computing Gröbner Bases and Free Resolutions of OI-Modules
Michael Morrow, Uwe Nagel
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Given a sequence of related modules Mₙ defined over a sequence of related polynomial rings, one may ask how to simultaneously compute a finite Gr\"obner basis for each Mₙ. Furthermore, one may ask how to simultaneously compute the module of syzygies of each Mₙ. In this paper we address both questions. Working in the setting of OI-modules over a Noetherian polynomial OI-algebra, we provide OI-analogues of Buchberger's Criterion, Buchberger's Algorithm for computing Gr\"obner bases, and Schreyer's Theorem for computing syzygies. We also establish a stabilization result for Gr\"obner bases.
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