Intersection of ideals in a polynomial ring over a dual valuation domain
type: Item
instance of: scholarly article
title: Intersection of ideals in a polynomial ring over a dual valuation domain
zbMATH Open document ID: 1476.14101
DOI: 10.1155/2018/9316901
author: Regis F. Babindamana
author: Andre S. E. Mialebama Bouesso
published in: Journal of Mathematics
publication date: 2019-02-26T00:00:00Z
review text: A dual valuation ring is a ring of the form \(\mathbf{A}= \mathbf{V} + \epsilon \mathbf{V} \cong \mathbf{V}[\epsilon]/\langle{\epsilon^2}\rangle\), where \(\mathbf{V} \) is a valuation domain. The authors propose a method for computing strong Gröbner bases for finitely-generated ideals of \(\mathbf{A}[X_1,\ldots,X_n]\). As application, they compute finite generating sets for syzygy modules over \(\mathbf{A}[X_1,\ldots,X_n]\) as well as for the intersection of two finitely-generated ideals of \(\mathbf{A}[X_1,\ldots,X_n]\). Since it is now known that the existence of finite Groebner bases for finitely-generated ideals of \(\mathbf{V}[X_1,\ldots,X_n]\) (\(\mathbf{V}\) being a valuation domain) is only guaranteed in case \(\mathbf{V}\) has Krull dimension \(\leq 1\), the authors may have forgotten to mention that condition.
reviewed by: Ihsen Yengui
Mathematics Subject Classification ID: 14Q20
Mathematics Subject Classification ID: 03F65
zbMATH DE Number: 7029808
zbMATH Keywords: dual Valuation ring
zbMATH Keywords: Groebner bases
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9316901
OpenAlex ID: W2901351907
cites work: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
cites work: Q4305609
cites work: Noncommutative Gröbner Bases over Rings
cites work: Dynamical Gröbner bases
cites work: Constructive commutative algebra. Projective modules over polynomial rings and dynamical Gröbner bases
cites work: Relèvements des structures symplectiques et pseudo-riemanniennes à des variétés de points proches
cites work: A First Course in Computational Algebraic Geometry
cites work: SINGULAR
cites work: Q3413659
description: scientific article; zbMATH DE number 7029808