@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} }