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Paper   IPM / M / 8541
School of Mathematics
  Title:   Comaximal graph of commutative rings
1.  H. R. Maimani
2.  S. Yassemi (Joint with M. Salimi and A. Sattari)
  Status:   Published
  Journal: J. Algebra
  Vol.:  319
  Year:  2008
  Pages:   1801–1808
  Supported by:  IPM
Let R be a commutative ring with identity. Let Γ(R) be a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if Ra + Rb = R. In this paper we consider a subgraph Γ2(R) of Γ(R) which consists of non-unit elements. We look at the connectedness and the diameter of this graph. We completely characterize the diameter of the graph Γ2(R)\J(R). In addition, it is shown that for two finite semi-local rings R and S, if R is reduced, then Γ(R) ≅ Γ(S) if and only if RS.

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