Some properties of comaximal ideal graph of a commutative ring

Document Type : Research Paper

Authors

Islamic Azad University, Central Tehran Branch

Abstract

Let $R$ be a commutative ring with identity‎. ‎We use‎ ‎$\varphi (R)$ to denote the comaximal ideal graph‎. ‎The vertices‎ ‎of $\varphi (R)$ are proper ideals of R which 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 planarity of line graph‎ ‎associated to $\varphi (R)$‎.

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References

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History

  • Receive Date: 12 April 2016
  • Revise Date: 07 September 2016
  • Accept Date: 25 October 2016
  • Published Online: 01 March 2017

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