Armendariz Property of $k[x,y]$ Modulo Monomial Ideals
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@Article{CMR-38-422,
author = {Guo , YingDu , Xiankun and Xu , Xiaowei},
title = {Armendariz Property of $k[x,y]$ Modulo Monomial Ideals},
journal = {Communications in Mathematical Research },
year = {2022},
volume = {38},
number = {3},
pages = {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 $I.$
}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2022-0005}, url = {http://global-sci.org/intro/article_detail/cmr/20963.html} }
TY - JOUR
T1 - Armendariz Property of $k[x,y]$ Modulo Monomial Ideals
AU - Guo , Ying
AU - Du , Xiankun
AU - Xu , Xiaowei
JO - Communications in Mathematical Research
VL - 3
SP - 422
EP - 430
PY - 2022
DA - 2022/08
SN - 38
DO - http://doi.org/10.4208/cmr.2022-0005
UR - https://global-sci.org/intro/article_detail/cmr/20963.html
KW - Armendariz ring, polynomial ring, monomial ideal.
AB -
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 $I.$
Ying Guo, Xiankun Du & Xiaowei Xu. (2022). Armendariz Property of $k[x,y]$ Modulo Monomial Ideals.
Communications in Mathematical Research . 38 (3).
422-430.
doi:10.4208/cmr.2022-0005
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