The annihilator-inclusion Ideal graph of a commutative ring

Communications in Combinatorics and Optimization

article

Amjadi, J.¹  Khoeilar, R.¹  Alilou, A.² 

[1] Azarbaijan Shahid Madani University;Jabir Ibn Hayyan research center

关键词: Annihilator-inclusion ideal graph;    Artinian ring;    planar graph;    genus;   

DOI  :  10.22049/cco.2020.26752.1139

学科分类：社会科学、人文和艺术（综合）

来源: Azarbaijan Shahide Madani Universit

【 摘 要 】

Let R be a commutative ring with non-zero identity. The annihilatorinclusion ideal graph of R, denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of R and two distinct vertices I and J are adjacent if and onlyif either Ann(I) ⊆ J or Ann(J) ⊆ I. The purpose of this paper is to provide somebasic properties of the graph ξR. In particular, shows that ξR is a connected graphwith diameter at most three, and has girth 3 or ∞. Furthermore, is determined allisomorphic classes of non-local Artinian rings whose annihilator-inclusion ideal graphshave genus zero or one.

【 授权许可】

CC BY-SA