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http://dx.doi.org/10.4134/BKMS.2012.49.5.1015

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

Zhao, Ping (School of Mathematics and Computer Science GuiZhou Normal University, Mathematics Teaching & Research Section Guiyang Medical College)
Yang, Mei (Department of Petroleum Engineering Texas A&M University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 1015-1025 More about this Journal
Abstract
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 $CPO_n$.
Keywords
order-preserving transformations; compression-preserving transformations; Green's relations;
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