Balanced Zero-Divisor Graphs of Matrix Rings

被引：3

作者：

Miguel, C. ^{[1
]}

机构：

[1] Beira Interior Univ, Inst Telecomun, Dept Math, Covilha, Portugal

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2013年 / 34卷 / 02期

关键词：

finite ring; zero-divisor graph; principal ideal ring;

D O I：

10.1134/S1995080213020066

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a finite commutative ringwith identity. We prove that if R is a principal ideal ring then the directed zero-divisor graph Gamma(M-n(R)) is balanced and eulerian. We also find the smallest finite commutative ring R with identity such that Gamma(M-n(R)) is not balanced.

引用

页码：137 / 141

页数：5

共 14 条

[1] On zero-divisor graphs of finite rings
Akbari, S.
Mohammadian, A.
[J]. JOURNAL OF ALGEBRA, 2007, 314 (01) : 168 - 184
[2] Zero-divisor graphs of non-commutative rings
Akbari, S
Mohammadian, A
[J]. JOURNAL OF ALGEBRA, 2006, 296 (02) : 462 - 479
[3] The zero-divisor graph of a commutative ring
Anderson, DF
Livingston, PS
[J]. JOURNAL OF ALGEBRA, 1999, 217 (02) : 434 - 447
[4] COLORING OF COMMUTATIVE RINGS
BECK, I
[J]. JOURNAL OF ALGEBRA, 1988, 116 (01) : 208 - 226
[5] Zero-Divisor Graphs of Matrices Over Commutative Rings
Bozic, Ivana
Petrovic, Zoran
[J]. COMMUNICATIONS IN ALGEBRA, 2009, 37 (04) : 1186 - 1192
[6] Brown W. C., 1993, MONOGRAPHS TXB PURE, V169
[7] Fine B., 1993, MATH MAG, V66, P248
[8] Gatalevich A., 1999, J MATH SCI NEW YORK, V96, P3013
[9] Gibbons Alan, 1985, ALGORITHMIC GRAPH TH
[10] ELEMENTARY DIVISORS AND MODULES
KAPLANSKY, I
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 66 (JUL-) : 464 - 491

← 1 2 →