![Armendariz Property of $k[x,y]$ Modulo Monomial Ideals](https://global-sci.com/images/articles/81490.png?w=900&h=&fit=&c=2&assets_cache=20241112054548&bg=white)
Year: 2022
Author: Ying Guo, Xiankun Du, Xiaowei Xu
Communications in Mathematical Research , Vol. 38 (2022), Iss. 3 : pp. 422–430
Abstract
In this paper, we give equivalent conditions for the factor rings of the polynomial ring $k[x,y]$ modulo monomial ideals to be Armendariz rings, where $k$ is a field. For an ideal $I$ with 2 or 3 monomial generators, or $n$ homogeneous monomial generators, such that $k[x,y]/I$ is an Armendariz ring, we characterize the minimal generator set $G(I)$ of $I.$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2022-0005
Communications in Mathematical Research , Vol. 38 (2022), Iss. 3 : pp. 422–430
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Armendariz ring polynomial ring monomial ideal.