Zero-divisor graphs of unitary R-modules over commutative rings

被引：0

作者：

Aijaz, M. ^{[1
]}

Pirzada, S. ^{[2
]}

Somasundaram, A. ^{[3
]}

机构：

[1] Lovely Profess Univ, Dept Comp Sci Engn, Phagwara, Punjab, India

[2] Univ Kashmir, Dept Math, Srinagar, India

[3] Birla Inst Technol & Sci, Dept Gen Sci, Pilani, Rajasthan, India

来源：

AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS | 2022年 / 19卷 / 01期

关键词：

Module; ring; zero divisor graph of module; complete graph; diameter; clique;

D O I：

10.1080/09728600.2022.2058895

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a commutative ring with unity 1 not equal 0 and let M be a unitary R-module. In this paper, we derive some completeness conditions on the zero divisor graphs of modules over commutative rings. It is shown that the weak zero divisor graph of a simple R-module is complete if and only if R is a field. We investigate the zero divisor graphs in finitely generated R-modules. We find the diameter, the girth, the clique number and the vertex degrees of the zero-divisor graphs of the rings of integer modulo n as Z-modules.

引用

页码：69 / 73

页数：5