REGULARITY AND GREEN'S RELATIONS ON SEMIGROUPS OF TRANSFORMATION PRESERVING ORDER AND COMPRESSION

Abstract

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