摘要
讨论了环的半素理想的性质 ,并得到用素理想表示半素理想的如下结论 :( 1 )环 R的理想 Q是半素理想当且仅当 Q可表示为一些素理想的交 ;( 2 )对环 R的任意半素理想 Q及任意 x∈ R -Q,存在素理想 P满足 x P Q;( 3 ) Artin交换环的任意半素理想都可表示为包含它的极小素理想的交 ,且这种表示是唯一的。
By discussing the property of semi prime ideals and obtaining the follow results of representing semi prime ideal by prime ideals:(1) ideal Q of the ring R be semi prime ideal if and only if Q can be written as intersection of some prime ideals;(2) for any semi prime ideal Q and x∈R-Q,there exist prime ideal P such that xPQ;(3) every semi prime ideal of Artin ring R can be written as finite intersection of minimal prime ideals and the represent is unique.
出处
《宝鸡文理学院学报（自然科学版）》
CAS
2002年第2期120-122,共3页
Journal of Baoji University of Arts and Sciences(Natural Science Edition)
关键词
理想
素理想
半素理想
ideal
prime ideal
semi prime iseal
