GROBNER BASES FOR MODULES OVER PRUFER DOMAINS

IF 0.2 4区数学 Q4 MATHEMATICS Mathematical Reports Pub Date : 2023-01-01 DOI:10.59277/mrar.2023.25.75.3.495

ZORAN Z. PETROVIC, MAJA ROSLAVCEV

引用次数: 0

Abstract

Let R be a Pr¨ufer domain of Krull dimension one. We prove the existence of Gr¨obner bases for finitely generated submodules of finitely generated free modules over R[X], where the term order is POT, or, “position over term”. In order to do this, we first prove that there is a Gr¨obner basis for finitely generated ideals in R[X], which is a special case of the main result. The proof is based on the results from [3]. In addition to this we show, in the case of valuation domains, that every Gr¨obner basis is actually a strong Gr¨obner basis

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格罗伯纳基的模块在更广泛的领域

设R是克鲁尔维数为1的普氏定义域。证明了R[X]上有限生成自由模的有限生成子模的Gr¨obner基的存在性，其中项序为POT，即“位置/项”。为了做到这一点，我们首先证明了R[X]中有限生成理想存在Gr¨obner基，这是主要结果的一种特殊情况。这个证明是基于[3]的结果。除此之外，我们还表明，在估值领域的情况下，每个格里奥布纳基础实际上都是一个强大的格里奥布纳基础

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Reports MATHEMATICS-

CiteScore

0.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal MATHEMATICAL REPORTS (formerly STUDII SI CERCETARI MATEMATICE) was founded in 1948 by the Mathematics Section of the Romanian Academy. It appeared under its first name until 1998 and received the name of Mathematical Reports in 1999. It is now published in one volume a year, consisting in 4 issues. The current average total number of pages is 500. Our journal MATHEMATICAL REPORTS publishes original mathematical papers, written in English. Excellent survey articles may be also accepted. The editors will put strong emphasis on originality, quality and applicability.

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