完全的伪效应代数  

Perfect pseudo effect algebras

作　　者：郭建胜[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）》2010年第6期9-13,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(60873119);中央高校基本科研业务费专项基金资助项目(GK200902047)

摘　　要：引入了完全的伪效应代数,给出了伪效应代数中理想、极大理想、素理想和值等概念.证明了伪效应代数中的每个值都有一个覆盖,所有的理想之集组成的集合是一个分配格;给出了伪效应代数中无限小元的概念和无限小元之集Infinit(E)等于极大理想之交Rad(E)的条件;证明了存在定向的插入偏序群范畴GI和完全的伪效应代数范畴PPEA之间的诚实的满的函子,完全的伪效应代数是整数群和定向插入偏序群的字典序乘积中的一个区间.Perfect pseudo effect algebras are introduced,and ideals,maximal ideals,prime ideals and values are defined.It is proved that every value in a pseudo effect algebra has a cover,the set of all ideals is a distributive lattice.The definition of an infinitesimal element is introduced,and some conditions for the set Infinit（E） be equal to the intersection Rad（E） of all maximal ideals are obtained,it is proved there exists a faithful and full functor from the category of directed interpolation po-groups GI into the category of perfect pseudo effect algebras PPEA and every perfect pseudo effect algebra is an interval in the lexicographical product of the group of all integers with a directed interpolation po-group.

关 键 词：伪效应代数 完全的伪效应代数 Riesz分解性质 理想 无穷小元 函子 

分 类 号：O153.1[理学—数学] O152.2[理学—基础数学]