(untitled) (Communications in Mathematical Research, 2022)
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.