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

Title & Authors
REGULARITY AND GREEN'S RELATIONS ON SEMIGROUPS OF TRANSFORMATION PRESERVING ORDER AND COMPRESSION
Zhao, Ping; Yang, Mei;

Abstract
Let $\small{[n]=\{1,2,{\cdots},n\}}$, and let $\small{PO_n}$ be the partial order-preserving transformation semigroup on [n]. Let $\small{CPO_n=\{{\alpha}{\in}PO_n:({\forall}x,y{\in}dom{\alpha}),\;|x{\alpha}-y{\alpha}|{\leq}|x-y|\}}$ Then $\small{CPO_n}$ is a subsemigroup of $\small{PO_n}$. In this paper, we characterize Green's relations and the regularity of elements for $\small{CPO_n}$.
Keywords
order-preserving transformations;compression-preserving transformations;Green's relations;
Language
English
Cited by
1.
COREGULARITY OF ORDER-PRESERVING SELF-MAPPING SEMIGROUPS OF FENCES,;;

대한수학회논문집, 2015. vol.30. 4, pp.349-361
1.
COREGULARITY OF ORDER-PRESERVING SELF-MAPPING SEMIGROUPS OF FENCES, Communications of the Korean Mathematical Society, 2015, 30, 4, 349
2.
Regular subsemigroups of the semigroups of transformations preserving a fence, Asian-European Journal of Mathematics, 2016, 09, 01, 1650003
3.
REGULARITY OF TRANSFORMATION SEMIGROUPS DEFINED BY A PARTITION, Communications of the Korean Mathematical Society, 2016, 31, 2, 217
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