A note on comaximal ideal graph of commutative rings
نویسندگان
چکیده
منابع مشابه
A note on a graph related to the comaximal ideal graph of a commutative ring
The rings considered in this article are commutative with identity which admit at least two maximal ideals. This article is inspired by the work done on the comaximal ideal graph of a commutative ring. Let R be a ring. We associate an undirected graph to R denoted by mathcal{G}(R), whose vertex set is the set of all proper ideals I of R such that Inotsubseteq J(R), where J(R) is...
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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 a...
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Acknowledgments I would like to begin by thanking my advisor, Professor Alexander Diesl, for his encouragement and excitement for my research. He has always remained supportive and interested in my work, and his many questions have kept me motivated and excited about my project. I would like to thank him as well for being understanding about my silly questions, helping me piece apart my convolu...
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The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.
متن کاملSome results on a supergraph of the comaximal ideal graph of a commutative ring
Let R be a commutative ring with identity such that R admits at least two maximal ideals. In this article, we associate a graph with R whose vertex set is the set of all proper ideals I of R such that I is not contained in the Jacobson radical of R and distinct vertices I and J are joined by an edge if and only if I and J are not comparable under the inclusion relation. The aim of this article ...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2020
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2019.06.004