摘要
对于每一个含有最小元素0的偏序集(P,≤)可以得到一个与其关联的图G(P).本文主要通过代数的方法研究了所得关联图G(P)的性质,证明了如果G(P)的色数和团数是有限的,那么色数和团数都仅比P的极小素理想的个数大1.
For any partially ordered set（P,≤） with a least element 0,there is a graph associated to it.The main purpose of this paper is using an algebraic method to study the properties of the associated graphs.It is proved that if the chromatic number and the clique number of the associated graph are finite,then they are both larger than the number of minimal prime ideals of P only one.
出处
《纯粹数学与应用数学》
CSCD
2010年第4期615-619,625,共6页
Pure and Applied Mathematics
基金
国家自然科学基金(60974082)
国家重点实验室综合业务网络基金(ISN02080003)
关键词
偏序集
色数
团数
理想
partially ordered set
chromatic number
clique number
ideal
