THE ZERO-DIVISOR GRAPH OF A COMMUTATIVE RING WITHOUT IDENTITY

被引：17

作者：

Anderson, David F. ^{[1
]}

Weber, Darrin ^{[2
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Univ Evansville, Dept Math, Evansville, IN 47722 USA

来源：

INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA | 2018年 / 23卷

关键词：

Zero-divisor graph; commutative ring without identity;

D O I：

10.24330/ieja.373663

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative ring. The zero-divisor graph of R is the (simple) graph Gamma(R) with vertices the nonzero zero-divisors of R, and two distinct vertices x and y are adjacent if and only if xy = 0. In this article, we investigate Gamma(R) when R does not have an identity, and we determine all such zero-divisor graphs with 14 or fewer vertices.

引用

页码：176 / 202

页数：27

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