文章基本信息

标题：On the girth of regular digraph of ideals of an Artinian ring
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作者：Masoud Karimi
期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2015
卷号：12
期号：2-3
页码：177-179
DOI：10.1016/j.akcej.2015.11.012
语种：English
出版社：Elsevier
摘要：AbstractLetRbe a commutative ring. The regular digraph of ideals ofR, denoted byΓ(R), is a digraph whose vertex-set is the set of all non-trivial ideals ofRand, for every two distinct verticesIandJ, there is an arc fromItoJ, wheneverIcontains an elementxsuch thatxy≠0for ally∈J.In this article we show that an indecomposable Noetherian ringRis Artinian local if and only ifZ(I)=Z(R)for every non-nilpotent idealIand deduce that the girth ofΓ(R)is not equal to four.
关键词：KeywordsenCommutative ringGirthRegular digraphZero divisor