On the comaximal ideal graph of a commutative ring | Zendy

Mehrdad Azadi | Zendy; Z. Jafari | Zendy; Changiz Eslahchi | Zendy

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On the comaximal ideal graph of a commutative ring

Author(s) -

Mehrdad Azadi,

Z. Jafari,

Changiz Eslahchi

Publication year - 2016

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1505-23

Subject(s) - mathematics , planarity testing , commutative ring , jacobson radical , combinatorics , graph , ideal (ethics) , radical of an ideal , associated prime , primary ideal , discrete mathematics , principal ideal ring , commutative property , ring (chemistry) , law , prime (order theory) , chemistry , organic chemistry , political science

Let $R$ be a commutative ring with identity. We use $\Gamma ( R )$ to denote the comaximal ideal graph. The vertices of $\Gamma ( R )$ are proper ideals of R that are not contained in the Jacobson radical of $R$, and two vertices $I$ and $J$ are adjacent if and only if $I + J = R$. In this paper we show some properties of this graph together with the planarity and perfection of $\Gamma ( R )$.

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