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Volume 38, Issue 3
Armendariz Property of $k[x,y]$ Modulo Monomial Ideals

Ying Guo, Xiankun Du & Xiaowei Xu

DOI: 10.4208/cmr.2022-0005

Commun. Math. Res., 38 (2022), pp. 422-430.

Published online: 2022-08

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  • 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 $I.$

  • Keywords

Armendariz ring, polynomial ring, monomial ideal.

  • AMS Subject Headings

16S36, 16D25

  • Copyright

COPYRIGHT: © Global Science Press

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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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