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 - <p style="text-align: justify;">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 $I.$</p>