FZ-Domain的基与抽象基的RZ-理想完备化  

The RZ-ideal completions of FZ-directed basis and FZ-abstract basis for FZ-Domains

作　　者：刘敏[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2011年第2期8-12,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10871121;11001158)

摘　　要：在FZ-Domain中引入FZ-定向基与FZ-抽象基的概念,研究了它们的RZ-理想完备化.证明了:对一类子集系统,一个FZ-Domain的FZ-定向基的定向RZ-理想完备化同构于该FZ-Domain;偏序集P是FZ-Domain当且仅当存在一个FZ-抽象基B使得P同构于B的定向的RZ-理想完备化.The concepts of FZ-Directed basis and FZ-abstract basis for FZ-Domains are defined.The RZ-ideal completions of them are studied.It is proved that for one class of subset systems,every FZ-Domain is isomorphic to the direct round Z-ideal completion of its FZ-directed basis;and a poset P is an FZ-Domain if and only if there exists an FZ-abstract basis B such that P is isomorphic to the direct RZ-ideal completion of B.

关 键 词：FZ-Domain 子集系统 FZ-基 FZ-抽象基 RZ-理想完备化 

分 类 号：O153.1[理学—数学]