REGULARITY AND GREEN'S RELATIONS ON SEMIGROUPS OF TRANSFORMATION PRESERVING ORDER AND COMPRESSION
Ping Zhao, Mei Yang · Bulletin of the Korean Mathematical Society · 2012
Let $[n]=\{1,2,{\cdots},n\}$ , and let $PO_n$ be the partial order-preserving transformation semigroup on [n]. Let $$CPO_n=\{{\alpha}{\in}PO_n:({\forall}x,y{\in}dom{\alpha}),\;|x{\alpha}-y{\alpha}|{\leq}|x-y|\}$$ Then $CPO_n$ is a subsemigroup of $PO_n$ . In this paper, we characterize Green's relations and the regularity of elements for $CPO_n$ .