On Graphs Related to Comaximal Ideals of a Commutative Ring
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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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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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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let $r$ be a commutative ring with identity. we use $varphi (r)$ to denote the comaximal ideal graph. the vertices of $varphi (r)$ are proper ideals of r which are not contained in the jacobson radical of $r$, and two vertices $i$ and $j$ are adjacent if and only if $i + j = r$. in this paper we show some properties of this graph together with planarity of line graph assoc...
متن کاملA Note on a graph associated to a commutative ring
The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings. In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$. In Section 2 of this articl...
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ژورنال
عنوان ژورنال: ISRN Combinatorics
سال: 2013
ISSN: 2090-8911
DOI: 10.1155/2013/354696