Regularity and Green's relations on semigroups of transformation preserving order and compression

摘要

Let $[n]={1,2,dots, n}$, and let $PO_n$ be the partial order-preserving transformation semigroup on $[n]$. Let $$CPO_n={lphain PO_n: ( orall x,yin {m dom}lpha), |xlpha -ylpha|leq |x-y| }.$$ Then $CPO_n$ is a subsemigroup of $PO_n$. In this paper, we characterize Green$^,$s relations and the regularity of elements for $CPO_n$.