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Turkish Journal of Mathematics

DOI

10.3906/mat-1602-52

Abstract

Let $X_{n}=\{1,2,\ldots,n\}$ with its natural order and let ${\cal T}_{n}$ be the full transformation semigroup on $X_{n}$. A map $\alpha\in{\cal T}_{n}$ is said to be order-preserving if, for all $x,y\in X_{n}$, $x\leq y\Rightarrow x\alpha\leq y\alpha$. The map $\alpha\in{\cal T}_{n}$ is said to be a contraction if, for all $x,y\in X_{n}$, $ x\alpha-y\alpha \leq x-y $. Let ${\cal CT}_{n}$ and ${\cal OCT}_{n}$ denote, respectively, subsemigroups of all contraction maps and all order-preserving contraction maps in ${\cal T}_{n}$. In this paper we present characterisations of Green's relations on ${\cal CT}_{n}$ and starred Green's relations on both ${\cal CT}_{n}$ and ${\cal OCT}_{n}$.

First Page

500

Last Page

507

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