与交换环相关的几类完全零化子理想图

Q4 Mathematics

Journal of Algebra and Related Topics Pub Date : 2021-06-01 DOI:10.22124/JART.2021.17227.1214

M. Adlifard, S. Payrovi

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引用次数: 0

摘要

设$R$是一个交换环，设$Bbb a（R）$是具有非零零零化子的$R$的所有理想的集合。$R$的零化子理想图被定义为图${A_I}（R）$，其顶点集$Bbb A（R）^*=Bbb B（R）集减去{0}$，并且两个不同的顶点$I$和$J$是相邻的当且仅当${rm-Ann}_R（IJ）neq{rm-Ann}_R。本文研究了一类环的${A_I}（R）$的完全性。

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Some classes of perfect annihilator-ideal graphs associated with commutative rings

Let $R$ be a commutative ring and let $Bbb A(R)$ bethe set of all ideals of $R$ with nonzero annihilator.The annihilator-ideal graph of $R$ is defined as the graph${A_I}(R)$ with the vertex set $Bbb A(R)^*=Bbb A(R)setminus{0}$ and twodistinct vertices $I$ and $J$ are adjacent if and only if${rm Ann}_R(IJ)neq{rm Ann}_R(I) cup{rm Ann}_R(J)$. In this paper, perfectness of${A_I}(R)$ for some classes of rings is investigated.

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来源期刊

Journal of Algebra and Related Topics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

16 weeks