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2 results on '"13D02, 13P10, 13C10, 13P20, 14Q20"'

1. The syzygy theorem for B\'ezout rings

Author

Gamanda, Maroua, Lombardi, Henri, Neuwirth, Stefan, and Yengui, Ihsen

Subjects
Mathematics - Commutative Algebra, 13D02, 13P10, 13C10, 13P20, 14Q20
Abstract

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., Comment: This version differs from the published version for the statement and proof of Theorem 5.5, the statement of Theorems 5.8 and 6.2, as well as the free resolution at the end of Example 6.7. The changes have been typeset in green

Published
2019
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2. The syzygy theorem for Bézout rings

Author

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
Full Text
View/download PDF

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