A note on a graph related to the comaximal ideal graph of a commutative ring
نویسندگان
چکیده
منابع مشابه
Some 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 ...
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...
متن کاملsome properties of comaximal ideal graph of a commutative ring
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 کاملThe annihilator-inclusion Ideal graph of a commutative ring
Let R be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of R , denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacentif and only if either Ann(I) ⊆ J or Ann(J) ⊆ I. In this paper, we investigate the basicproperties of the graph ξR. In particular, we showthat ξR is a connected grap...
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ژورنال
عنوان ژورنال: Algebraic structures and their applications
سال: 2017
ISSN: 2382-9761,2423-3447
DOI: 10.29252/asta.4.1.57