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

Ping Zhao|Mei Yang
대한수학회 (The Korean Mathematical Society)|2012.09|대한수학회보 (Bulletin of the KMS)|제49권 제5호|pp. 1015-1025

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참고문헌

키워드

Green's relationsorder-preserving transformationscompression-preserving transformations
주제분류수학

초록

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 $CPO_n$.

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 $CPO_n$.

참고문헌 (11)

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