Some results on the comaximal ideal graph of a commutative ring

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Subramanian Visweswaran¹  Jaydeep Parejiya¹ 

[1] Department of Mathematics, Saurashtra Univesity

关键词: Comaximal ideal graph;    Special principal ideal ring;    Planar graph;    Split graph;    Complement of a vertex in a graph;   

DOI  :  10.13069/jacodesmath.423751

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

The rings considered in this article are commutative with identity which admit at least two maximalideals. Let R be a ring such that R admits at least two maximal ideals. Recall from Ye and Wu (J.Algebra Appl. 11(6): 1250114, 2012) that the comaximal ideal graph of R, denoted by C (R) is anundirected simple graph whose vertex set is the set of all proper ideals I of R such that I 6⊆ J(R),where J(R) is the Jacobson radical of R and distinct vertices I1, I2 are joined by an edge in C (R) ifand only if I1 + I2 = R. In Section 2 of this article, we classify rings R such that C (R) is planar. InSection 3 of this article, we classify rings R such that C (R) is a split graph. In Section 4 of this article,we classify rings R such that C (R) is complemented and moreover, we determine the S-vertices ofC (R).

【 授权许可】

CC BY