Bulletin of the
Korean Mathematical Society BKMS

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

Keywords: order-preserving transformations, compression-preserving transformations, Green's relations

MSC numbers: 20M20