与交换环相关联的图上的注释

Q4 Mathematics
S. Visweswaran, J. Parejiya
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引用次数: 0

摘要

本文所考虑的环是可交换的。这篇文章的动机是关于环的共极大图的工作。在本文中,对于任何环$R$,我们将由$G(R)$表示的无向图相关联,其顶点集是$R$的所有元素的集合,并且不同顶点$x,y$通过$G(R)$中的边连接,当且仅当$Rxcap-Ry=Rxy$。在本文的第2节中,我们对环$R$进行了分类,使得$G(R)$是完备的,并且我们还考虑了确定环$R$chi(G(R))=ω(G(R,)本文章由计算机程序翻译,如有差异,请以英文原文为准。
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A 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 article, we classify rings $R$ such that $G(R)$ is complete and we also consider the problem of determining rings $R$ such that $chi(G(R)) = omega(G(R))< infty$. In Section 3 of this article, we classify rings $R$ such that $G(R)$ is planar.
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来源期刊
Journal of Algebra and Related Topics
Journal of Algebra and Related Topics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
0.60
自引率
0.00%
发文量
0
审稿时长
16 weeks
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