1. The syzygy theorem for Bézout rings
- Author
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Stefan Neuwirth, Ihsen Yengui, Henri Lombardi, Maroua Gamanda, Département de Mathematiques [Sfax], Faculté des Sciences de Sfax, Université de Sfax - University of Sfax-Université de Sfax - University of Sfax, Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), John Templeton Foundation (ID 60842), ANR-15-IDEX-0003,BFC,ISITE ' BFC(2015), Fédération Bourgogne Franche-Comté Mathématiques (BFC-Math ), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), and ANR: 15-IDEX-0003,BFC,ISITE « BFC(2015)
- Subjects
Pure mathematics ,[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] ,Schreyer's syzygy algorithm ,010103 numerical & computational mathematics ,01 natural sciences ,Constructive ,Valuation ring ,MSC 2010: 13D02, 13P10, 13C10, 13P20, 14Q20 ,Finitely-generated abelian group ,0101 mathematics ,Syzygy theorem ,Gröbner ring ,Monomial order ,strict Bézout ring ,Mathematics ,Algebra and Number Theory ,Hilbert's syzygy theorem ,Mathematics::Commutative Algebra ,monomial order ,valuation ring ,Applied Mathematics ,010102 general mathematics ,free resolution ,Divisibility rule ,Mathematics - Commutative Algebra ,16. Peace & justice ,dynamical Gröbner basis ,13D02, 13P10, 13C10, 13P20, 14Q20 ,Schreyer's monomial order ,Computational Mathematics - Abstract
International audience; 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 Bézout rings with a divisibility test for the case of finitely generated modules whose module of leading terms is finitely generated.
- Published
- 2019
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