A NOTE ON GRAPHICAL REPRESENTATION OF RINGS

被引：133

作者：

SHARMA, PK ^{[1
]}

BHATWADEKAR, SM ^{[1
]}

机构：

[1] TATA INST FUNDAMENTAL RES,SCH MATH,BOMBAY 400005,MAHARASHTRA,INDIA

来源：

JOURNAL OF ALGEBRA | 1995年 / 176卷 / 01期

关键词：

D O I：

10.1006/jabr.1995.1236

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative ring with identity. Let G be a graph with vertices as elements of R, where two distinct vertices x and y are adjacent if and only if Rx + Ry = R. In this paper we show that a commutative ring R is a finite ring if and only if the graph G (associated with R as above) is finitely colourable. Moreover we show that in this case the chromatic number of the graph G is the sum of the number of maximal ideals and the number of units of R. (C) 1995 Academic Press, Inc.

引用

页码：124 / 127

页数：4