Armendariz Property of $k[x,y]$ Modulo Monomial Ideals

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 $I.$