The syzygy theorem for Bézout rings
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- by Maroua Gamanda, Henri Lombardi, Stefan Neuwirth and Ihsen Yengui HTML | PDF
- Math. Comp. 89 (2020), 941-964
Abstract:
We provide constructive versions of Hilbert’s syzygy theorem for $\mathbb {Z}$ and $\mathbb {Z}/N\mathbb {Z}$ following Schreyer’s method. Moreover, we extend these results to arbitrary coherent strict Bézout rings with a divisibility test for the case of finitely generated modules whose module of leading terms is finitely generated.References
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Additional Information
- Maroua Gamanda
- Affiliation: Département de mathématiques, Faculté des sciences de Sfax, Université de Sfax, 3000 Sfax, Tunisia
- MR Author ID: 1235530
- Email: marwa.gmenda@hotmail.com
- Henri Lombardi
- Affiliation: Laboratoire de mathématiques de Besançon, Université Bourgogne Franche-Comté, 25030 Besançon Cedex, France
- MR Author ID: 277650
- Email: henri.lombardi@univ-fcomte.fr
- Stefan Neuwirth
- Affiliation: Laboratoire de mathématiques de Besançon, Université Bourgogne Franche-Comté, 25030 Besançon Cedex, France
- MR Author ID: 635157
- Email: stefan.neuwirth@univ-fcomte.fr
- Ihsen Yengui
- Affiliation: Département de mathématiques, Faculté des sciences de Sfax, Université de Sfax, 3000 Sfax, Tunisia
- MR Author ID: 657905
- Email: ihsen.yengui@fss.rnu.tn
- Received by editor(s): August 17, 2017
- Received by editor(s) in revised form: February 10, 2018, and May 11, 2019
- Published electronically: September 19, 2019
- Additional Notes: The third author was supported in part by the French “Investissements d’avenir” program, project ISITE-BFC (contract ANR-15-IDEX-03).
The fourth author was supported in part by the John Templeton Foundation (ID 60842). - © Copyright 2019 the authors
- Journal: Math. Comp. 89 (2020), 941-964
- MSC (2010): Primary 13D02; Secondary 13P10, 13C10, 13P20, 14Q20
- DOI: https://doi.org/10.1090/mcom/3466
- MathSciNet review: 4044457