The zero-divisor graph of a commutative ring

被引:1052
作者
Anderson, DF [1 ]
Livingston, PS [1 ]
机构
[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA
关键词
D O I
10.1006/jabr.1998.7840
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For each commutative ring R we associate a (simple) graph Gamma(R). We investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of Gamma(R). (C) 1999 Academic Press.
引用
收藏
页码:434 / 447
页数:14
相关论文
共 12 条
[1]   BECK COLORING OF A COMMUTATIVE RING [J].
ANDERSON, DD ;
NASEER, M .
JOURNAL OF ALGEBRA, 1993, 159 (02) :500-514
[2]  
[Anonymous], 2001, GRAPH THEORY
[3]  
[Anonymous], [No title captured]
[4]  
Atiyah M. F., 1969, Introduction To Commutative Algebra, Addison-Wesley series in mathematics
[5]   COLORING OF COMMUTATIVE RINGS [J].
BECK, I .
JOURNAL OF ALGEBRA, 1988, 116 (01) :208-226
[6]  
Diestel R., 1997, Graph Theory
[7]   PROPERTIES OF RINGS WITH A FINITE NUMBER OF ZERO DIVISORS [J].
GANESAN, N .
MATHEMATISCHE ANNALEN, 1964, 157 (03) :215-218
[8]  
Ganesan N., 1965, MATH ANN, V161, P241
[9]  
KAPLANSKY I, 1974, COMMUTATRIVE RINGS
[10]   ON PROPERTIES OF RINGS WITH A FINITE NUMBER OF ZERO DIVISORS [J].
KOH, K .
MATHEMATISCHE ANNALEN, 1967, 171 (01) :79-&