Commutative von Neumann regular rings are 1-Gröbner

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI:10.2298/aadm210419030p

Z. Petrovic, Maja Roslavcev

引用次数: 0

Abstract

Let R be a commutative von Neumann regular ring. We show that every finitely generated ideal I in the ring of polynomials R[X] has a strong Gr?bner basis. We prove this result using only the defining property of a von Neumann regular ring.

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交换冯·诺伊曼正则环是1-Gröbner

设R是一个交换冯·诺伊曼正则环。我们证明了多项式环R[X]中的每一个有限生成的理想I都具有强的Gr?bn。我们只用von Neumann正则环的定义性质证明了这个结果。

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

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).