![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
In this article, graph blow-up is used to study the implements of the co-maximal graph and the co-maximal ideal graph 𝒞(R) of a commutative ring R. We show that for a ring R with finitely many maximal ideals, the graph 𝒞(R) is a blow-up of a Boolean graph, and we give more detailed structure of the graphs
and 𝒞(R) as blow-ups of Boolean graphs. We determine for what rings R, 𝒞(R) or
is a finite graph, respectively. In the end, we get some new results for rings by taking advantage of the graph
.
ACKNOWLEDGMENTS
The authors express their sincere thanks to the anonymous referee for the careful reading and suggestions which improved the exposition of the article.
This research is supported by the National Natural Science Foundation of China (Grant No. 11271250). The third author is supported by the Youth Foundation of Shanghai (Grant No. sdl10017).
Notes
Communicated by I. Swanson.