A note on comaximal graph of non-commutative rings
نویسنده
چکیده
Let R be a ring with unity. The graph Γ(R) is a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if Ra + Rb = R. Let Γ2(R) is the subgraph of Γ(R) induced by the non-unit elements. H.R. Maimani et al. [H.R. Maimani et al., Comaximal graph of commutative rings, J. Algebra 319 (2008) 1801-1808] proved that: “If R is a commutative ring with unity and the graph Γ2(R)\J(R) is n-partite, then the number of maximal ideals of R is at most n.” The proof of this result is not correct. In this paper we present a correct proof for this result. Also we generalize some results given in the aforementioned paper for the non-commutative rings.
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