Some results on the complement of the annihilating ideal graph of a commutative ring

被引：5

作者：

Visweswaran, S. ^{[1
]}

Patel, Hiren D. ^{[1
]}

机构：

[1] Saurashtra Univ, Dept Math, Rajkot 360005, Gujarat, India

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2015年 / 14卷 / 07期

关键词：

The complement of the annihilating ideal graph of a commutative ring; maximal N-prime of (0); B-prime of (0); complemented graph; ZERO-DIVISOR GRAPH;

D O I：

10.1142/S0219498815500991

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Rings considered in this article are commutative with identity which admit at least one nonzero annihilating ideal. For such a ring R, we determine necessary and sufficient conditions in order that the complement of its annihilating ideal graph is connected and also find its diameter when it is connected. We discuss the girth of the complement of the annihilating ideal graph of R and prove that it is either equal to 3 or infinity. We also present a necessary and sufficient condition for the complement of the annihilating ideal graph to be complemented.

引用

页数：23

共 17 条

[11] NOETHERIAN-LIKE RINGS OF EVANS,EG
HEINZER, W
OHM, J
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 34 (01) : 73 - &
[12] Kaplansky I., 1974, Commutative rings
[13] The zero-divisor graph of Von Neumann regular rings
Levy, R
Shapiro, J
[J]. COMMUNICATIONS IN ALGEBRA, 2002, 30 (02) : 745 - 750
[14] SMARANDACHE VERTICES OF THE GRAPHS ASSOCIATED TO THE COMMUTATIVE RINGS
Rahimi, A. M.
[J]. COMMUNICATIONS IN ALGEBRA, 2013, 41 (05) : 1989 - 2004
[15] SOME RESULTS ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A COMMUTATIVE RING
Visweswaran, S.
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2011, 10 (03) : 573 - 595
[16] Visweswaran S., 2012, ISRN ALGEBRA, V2012
[17] Visweswaran S., 2011, ISRN ALGEBRA 2011, V2011

← 1 2 →