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 Regularity and Green's relations on semigroups of transformation preserving order and compression Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 1015-1025 https://doi.org/10.4134/BKMS.2012.49.5.1015Printed September 30, 2012 Ping Zhao and Mei Yang Guiyang Medical College, Texas A$\&$M University Abstract : 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 Downloads: Full-text PDF