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A note on co-maximal ideal graph of commutative rings

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. Abstract:
  3. Let R be a commutative ring with unity. The co-maximal ideal graph of R, denoted by Γ(.R), is a graph whose vertices are the proper ideals of R which are not contained in the Jacobson radical of R, and two vertices I1 and I2 are adjacent if and only if I1 +I2=R- We classify all commutative rings whose co-maximal ideal graphs are planar. In 2012 the following question was posed: If T(R) is an infinite star graph, can R be isomorphic to the direct product of a field and a local ring? In this paper, we give an affirmative answer to this question
  4. Keywords:
  5. Co-maximal ideal graph ; Star graph
  6. Source: Ars Combinatoria ; Volume 134 , 2017 , Pages 261-265 ; 03817032 (ISSN)
  7. URL: https://arxiv.org/abs/1307.5401