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Your search keyword '"Gröbner ring"' showing total 3 results
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3 results on '"Gröbner ring"'

1. The syzygy theorem for Bezout rings.

Author

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

Subjects
*GROBNER bases
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 Bézout rings with a divisibility test for the case of finitely generated modules whose module of leading terms is finitely generated. [ABSTRACT FROM AUTHOR]

Published
2020
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2. A zero-dimensional valuation ring is 1-Gröbner.

Author

Li, Dongmei, Liu, Jinwang, and Zheng, Licui

Subjects
*GROBNER bases, *VALUATION theory, *ARCHIMEDEAN property, *NOETHERIAN rings, *DIMENSIONAL analysis
Abstract

In this study, we consider the following conjecture and open problem: (1) A valuation ring R is 1-Gröbner if and only if R is an Archimedean ring; (2) Is a 1-Gröbner valuation ring coherent? First, we prove that a zero-dimensional valuation ring is 1-Gröbner. Furthermore, we give a positive answer to (1) and a negative answer to (2). Finally, we present an example of a valuation ring that is 1-Gröbner but not coherent or Noetherian. [ABSTRACT FROM AUTHOR]

Published
2017
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3. 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
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