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Research Article | Open Access

Some improvements for the algorithm of Gröbner bases over dual valuation domain

Licui Zheng, Dongmei Li( ), Jinwang Liu
Department of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China
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Abstract

As a special ring with zero divisors, the dual noetherian valuation domain has attracted much attention from scholars. This article aims at to improve the Buchberger's algorithm over the dual noetherian valuation domain. We present some criterions that can be applied in the algorithm for computing Gröbner bases, and the criterions may drastically reduce the number of S-polynomials in the course of the algorithm. In addition, we clearly demonstrate the improvement with an example.

Keywords

Gröbner basesdual noetherian valuation domainS-polynomials

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Electronic Research Archive
Volume 31 Issue 7,
July 2023
Pages 3999-4010
DOI: 10.3934/era.2023203

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Cite this article:
Zheng L, Li D, Liu J. Some improvements for the algorithm of Gröbner bases over dual valuation domain. Electronic Research Archive, 2023, 31(7): 3999-4010. https://doi.org/10.3934/era.2023203

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Received: 20 January 2023
Revised: 28 April 2023
Accepted: 08 May 2023
Published: 15 July 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)