真理想族的上、下确界及其性质  

The suprume and infium of a family of proper ideals and their properties

作　　者：马春晖[1,2] 李生刚[1] 伏文清[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 [2]西安建筑科技大学理学院,陕西西安710055

出　　处：《云南大学学报（自然科学版）》2009年第4期329-333,共5页Journal of Yunnan University(Natural Sciences Edition)

基　　金：陕西省自然科学基金资助项目(2007A12);西安建筑科技大学青年科技基金资助项目(QN0736)

摘　　要：研究了非空集合上真理想族的上、下确界.在非标准扩大模型中,采用单子论的研究方法,提出了非空集合上真理想族上、下确界的定义,在此基础上研究了真理想族上、下确界存在的充要条件,并得到了真理想族在上、下确界存在的条件下的一些运算性质.The suprume and infium of a family of proper ideals on anonempty set are studied. Meanwhile, the method of monad theory is used in the nonstandardenlarged model. And, the definition of the suprume and infium of a family ofproper ideals are introduced and some necessary and sufficient conditions oftheir existence are discussed. Furthermore, the properties of suprumeand infium of a family of proper ideals are obtained.

关 键 词：真理想 非标准扩大模型 上确界 单子 

分 类 号：O141.41[理学—数学] O189.11[理学—基础数学]