分组函数的代数性质与序和  

Algebraic Properties and Ordinal Sum of Grouping Functions

作　　者：张廷海[1] 覃锋[1] ZHANG Tinghai;QIN Feng(College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China)

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022

出　　处：《吉林大学学报（理学版）》2019年第3期480-486,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61563020);江西省自然科学重点项目基金(批准号:20171ACB20010);江西省教育厅科技项目(批准号:60296)

摘　　要：考虑分组函数的幂等性、严格单调性、阿基米德性等基本代数性质的相互关系,通过类似半群序和的结构给出一簇分组函数的序和还是分组函数的性质,并纠正了已有文献在刻画重叠函数上述性质时的几处错误.We considered the interrelations among the basic algebraic properties of grouping functions, such as idempotency, strict monotonicity, Archimedean property. We gave the results that the ordinal sum of a series of grouping functions was still a grouping function by means of a way similar to the ordinal sum of semigroups. Furthermore, we rectified several errors in describing the above properties about overlap functions in the existing literature.

关 键 词：分组函数 幂等元 极限条件 阿基米德性 序和 

分 类 号：O159[理学—数学]