ON THE IDEAL-BASED ZERO-DIVISOR GRAPHS

被引：3

作者：

Ansari-Toroghy, H. ^{[1
]}

Farshadifar, F. ^{[2
]}

Mahboobi-Abkenar, F. ^{[1
]}

机构：

[1] Univ Guilan, Fac Math Sci, Dept Pure Math, Rasht, Iran

[2] Farhangian Univ, Tehran, Iran

来源：

INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA | 2018年 / 23卷

关键词：

Zero-divisor; coreduced; complemented;

D O I：

10.24330/ieja.373650

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative ring. In this paper, we study the annihilator ideal-based zero-divisor graph by replacing the ideal I of R with the ideal AnnR (M) for an R-module M. Also, we investigate a certain subgraph of the annihilator ideal-based zero-divisor graph and obtain some related results.

引用

收藏

页码：115 / 130

页数：16

相关论文

共 25 条

[1] THE ANNIHILATING-IDEAL GRAPH OF A COMMUTATIVE RING WITH RESPECT TO AN IDEAL [J].

Aliniaeifard, F. ;

Behboodi, M. ;

Mehdi-Nezhad, E. ;

Rahimi, A. M. .

COMMUNICATIONS IN ALGEBRA, 2014, 42 (05) :2269-2284

[2] On the diameter of the graph ΓAnn(M)(R) [J].

Anderson, David F. ;

Ghalandarzadeh, Shaban ;

Shirinkam, Sara ;

Rad, Parastoo Malakooti .

FILOMAT, 2012, 26 (03) :623-629

[3] BECK COLORING OF A COMMUTATIVE RING [J].

ANDERSON, DD ;

NASEER, M .

JOURNAL OF ALGEBRA, 1993, 159 (02) :500-514

[4] Zero-divisor graphs, von Neumann regular rings, and Boolean algebras [J].

Anderson, DF ;

Levy, R ;

Shapiro, J .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2003, 180 (03) :221-241

[5]

Anderson DF, 2001, LECT NOTES PURE APPL, V220, P61

[6] The zero-divisor graph of a commutative ring [J].

Anderson, DF ;

Livingston, PS .

JOURNAL OF ALGEBRA, 1999, 217 (02) :434-447

[7] The dual notion of multiplication modules [J].

Ansari-Toroghy, H. ;

Farshadifar, F. .

TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (04) :1189-1201

[8] ON THE DUAL NOTION OF PRIME RADICALS OF SUBMODULES [J].

Ansari-Toroghy, H. ;

Farshadifar, F. .

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2013, 6 (02)

[9] On the Dual Notion of Prime Submodules [J].

Ansari-Toroghy, H. ;

Farshadifar, F. .

ALGEBRA COLLOQUIUM, 2012, 19 :1109-1116

[10] THE DUAL NOTIONS OF SOME GENERALIZATIONS OF PRIME SUBMODULES [J].

Ansari-Toroghy, H. ;

Farshadifar, F. .

COMMUNICATIONS IN ALGEBRA, 2011, 39 (07) :2396-2416