无限集上严格保序变换半群的正则元及格林关系  

Regular elements and Green's relations of strictly order-preserving transformation semigroup on an infinite set

作　　者：许新斋[1] 孟玲[2] 

机构地区：[1]山东师范大学数学科学学院,山东济南250014 [2]山东工业职业学院基础部,山东淄博256414

出　　处：《纯粹数学与应用数学》2011年第3期297-301,共5页Pure and Applied Mathematics

基　　金：山东省中青年科学家科研奖励基金(2008BS01016)

摘　　要：设X是一个全序集,SOX是X上的严格保序变换半群.考虑X是一个全序无限集的情形.讨论了SOX中的正则元和SOX上的格林关系.证明了SOX中的元素α是正则的当且仅当α是双射.还证明了SOX的所有正则元形成SOX的一个极大子群.另外,给出了SOX上的格林关系L,R,D和H的刻划.SOX上格林关系的刻画对SOX的研究起重要作用.Let X be a totally ordered set and SOX the strictly order-preserving transformation semigroup on X.In this paper,the set X under consideration is a totally ordered infinite set.The regular elements in SOX and the green＇s relations on SOX are discussed.It is shown that an element α in SOX is regular if and only if α is a bijection.It is also shown that all regular elements of SOX form a maximal subgroup of SOX.In addition,characterizations for the green＇s relations L,R,D and H on SOX are given.The characterizations of green＇s relations on SOX play an importent role for study of SOX.

关 键 词：严格保序变换半群 正则元 格林关系 

分 类 号：O152.7[理学—数学]