Regular elements and Green's relations of strictly order-preserving transformation semigroup on an infinite set
XU Xin-zhai · 2011
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.