A survey on the Intersection graphs of ideals of rings

Communications in Combinatorics and Optimization

article

Chakrabarty, Ivy¹  Kureethara, Joseph Varghese² 

[1] Independent Researcher;Christ University

关键词: Ring;    ideal of a ring;    intersection graph;    genus;    chromatic number;   

DOI  :  10.22049/cco.2021.26990.1176

学科分类：社会科学、人文和艺术（综合）

来源: Azarbaijan Shahide Madani Universit

【 摘 要 】

Let L (R) denote the set of all non-trivial left ideals of a ring R. Theintersection graph of ideals of a ring R is an undirected simple graph denoted by G(R)whose vertices are in a one-to-one correspondence with L (R) and two distinct verticesare joined by an edge if and only if the corresponding left ideals of R have a non-zerointersection. The ideal structure of a ring reflects many ring theoretical properties.There is so much research that has been conducted during the last decade to explorethe properties of G(R). This is a survey of the developments in the study on theintersection graphs of ideals of rings since its introduction in 2009.

【 授权许可】

CC BY-SA