The Classification of the Annihilating-Ideal Graphs of Commutative Rings

被引：36

作者：

Aalipour, G. ^{[1
,2
]}

Akbar, S. ^{[1
,2
]}

Behboodi, M. ^{[2
,3
]}

Nikandish, R. ^{[2
,4
]}

Nikmehr, M. J. ^{[4
]}

Shaveisi, F. ^{[2
,5
]}

机构：

[1] Sharif Univ Technol, Dept Math Sci, Tehran, Iran

[2] IPM, Inst Res Fundamental Sci, Sch Math, Tehran, Iran

[3] Isfahan Univ Technol, Dept Math Sci, Esfahan, Iran

[4] KN Tossi Univ Technol, Fac Sci, Dept Math, Tehran, Iran

[5] Razi Univ, Fac Sci, Dept Math, Kermanshah, Iran

来源：

ALGEBRA COLLOQUIUM | 2014年 / 21卷 / 02期

关键词：

annihilating-ideal graph; clique number; chromatic number; Artinian ring; Noetherian ring; ZERO-DIVISOR GRAPHS;

D O I：

10.1142/S1005386714000200

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a commutative ring and A(R) be the set of ideals with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(R)backslash{(0)} and two distinct vertices I and J are a djacent if and only if IJ = (0). Here were present some results on the clique number and the chromatic number of the annihilating-ideal graph of a commutative ring. It is shown that if R is an Artinian ring and omega(AG(R)) = 2, then R is Gorenstein. Also, we investigate commutative rings who seannihilating-ideal graphs arecomplete or bipartite.

引用

页码：249 / 256

页数：8

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