Generic Gröbner bases and Weierstrass bases of homogeneous submodules of graded free modules
type: Item
instance of: scholarly article
title: Generic Gröbner bases and Weierstrass bases of homogeneous submodules of graded free modules
zbMATH Open document ID: 0972.13019
DOI: 10.1016/S0022-4049(99)00131-0
author: Mutsumi Amasaki
published in: Journal of Pure and Applied Algebra
publication date: 2000-11-21T00:00:00Z
review text: Let \(R=k[x_1, \dots, x_r]\) be a polynomial ring over an infinite field \(k\), and let \(E\) be a finitely generated, homogeneous submodule of arbitrary rank of a graded free \(R\)-module. This paper contains a new proof that there exists a generic Gröbner basis of \(E\) with respect to reverse lexicographic order with ``term over position'', which is also a Weierstrass basis for \(E\). It uses the structure theorem of finitely generated modules over a principal ideal domain. The existence of a Weierstrass basis for \(E\) was proven earlier by the author.
reviewed by: Reinhard Laubenbacher
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 1517286
zbMATH Keywords: polynomial ring
zbMATH Keywords: generic Gröbner basis
zbMATH Keywords: Weierstrass basis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1517286