强理想及其在有限偏序集上的应用  

Some applications of strong ideals on finite posets

作　　者：唐照勇 姜广浩[1] 刘志禹 

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《天津师范大学学报（自然科学版）》2017年第6期6-10,共5页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11361028);安徽高等学校省级自然科学研究重点资助项目(KJ2013A236;KJ2016A648;KJ2017A378);淮北师范大学研究生创新基金资助项目(2017yjscx07)

摘　　要：在偏序集上引入强集和强理想的概念,进而从另一个角度给出有限偏序集上元素之间的一种等价关系:连通关系,从而将有限偏序集分为连通和非连通两类.此外,在不交并偏序集上给出分支、可分分支和不可分分支等概念,并在有限偏序集上探讨强理想、非连通偏序集和不交并偏序集之间的关系.The concepts of strong set, strong ideal on posets are introduced. An equivalence relation between elements is given on a finite poser ： connecting relationship from another angle. And thus, finite posers are divided into two categories ： connecting posets and disconnected posets. In addition, the definitions of branch, separable branch and inseparable branch are also given on disjoint poset. Finally, the relationships of strong ideal, disconnected poser, disjoint poset on finite poset are discussed.

关 键 词：强集 强理想 连通关系 非(连通)有限偏序集 不交并偏序集 

分 类 号：O153.1[理学—数学]