Commutative von Neumann regular rings are 1-Gröbner

Applicable Analysis and Discrete Mathematics

article

Zoran Z. Petrović¹  Maja Roslavcev² 

[1] Faculty of Mathematics,University of Belgrade;Faculty of Mathematics, University of Belgrade

关键词: Gröbner bases;    Von Neumann regular ring;   

DOI  :  10.2298/AADM210419030P

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Let R be a commutative von Neumann regular ring. We show that everyfinitely generated ideal I in the ring of polynomials R[X] has a strong Gr¨obnerbasis. We prove this result using only the defining property of a von Neumannregular ring.

【 授权许可】

Unknown