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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)
  • Received : 2011.05.31
  • Published : 2012.09.30

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 $CPO_n$.

Acknowledgement

Supported by : Natural Science Fund of Guizhou

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