2010/07/20 by Saieed Akbari, Akbari, S., Mohammad Habibi +5
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1007.3361
openalex publication_date 2010/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)\backslash 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.