RINGS WHOSE ASSOCIATED EXTENDED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED

被引：0
作者：
Bennis, Driss [1 ]
EL Alaoui, Brahim [1 ]
L'hamri, Raja [1 ]
机构：
[1] Mohammad V Univ Rabat, Fac Sci, Dept Math, Rabat 10070, Morocco
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2024年 / 61卷 / 03期
关键词：
Commutative ring; zero-divisor graph; extended zero-divisor graph; complemented; uniquely complemented; zero-dimensional ring;
D O I：
10.4134/BKMS.b230348
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let R be a commutative ring with identity 1 not equal 0. In this paper, we continue the study started in [10] to further investigate when the extended zero-divisor graph of R, denoted as (Gamma) over bar (R), is complemented. We also study when (Gamma) over bar (R) is uniquely complemented. We give a complete characterization of when (Gamma) over bar (R) of a finite ring R is complemented. Various examples are given using the direct product of rings and idealizations of modules.
引用
收藏
页码：763 / 777
页数：15
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