The syzygy theorem for B\'ezout rings

Henri Lombardi; Ihsen Yengui; Maroua Gamanda; Stefan Neuwirth

The syzygy theorem for B\'ezout rings

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arxiv 1905.08117 v4 pith:2C6EJL7O submitted 2019-05-20 math.AC

Maroua Gamanda , Henri Lombardi , Stefan Neuwirth , Ihsen Yengui This is my paper · ORCID

classification math.AC

keywords ezoutfinitelygeneratedringssyzygytheoremarbitrarycase

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We provide constructive versions of Hilbert's syzygy theorem for Z and Z/nZ following Schreyer's method. Moreover, we extend these results to arbitrary coherent strict B\'ezout rings with a divisibility test for the case of finitely generated modules whose module of leading terms is finitely generated.

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Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings
math.AC 2024-11 accept novelty 7.0 of 10

Buchberger and Schreyer algorithms are generalized to strongly discrete coherent rings, with convergence characterized by finite generation of the leading term module.

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