On certain semigroups of full contractions of a finite chain

A. Umar; M. M. Zubairu

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arXiv · 1804.10057

On certain semigroups of full contractions of a finite chain

A. Umar·M. M. Zubairu

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Abstract

Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{T}_{n}$ be the semigroup of full transformations on $[n]$. Let $\mathcal{CT}_{n}=\{\alpha\in \mathcal{T}_{n}: (for ~all~x,y\in [n])~\left|x\alpha-y\alpha\right|\leq\left|x-y\right|\}$, then $\mathcal{CT}_{n}$ is a subsemigroup of $\mathcal{T}_{n}$. In this paper, we give a necessary and sufficient condition for an element to be regular and characterize all the Green's equivalences for the semigroup $\mathcal{CT}_{n}$. We further show that the semigroup $\mathcal{CT}_{n}$ is a left abundant semigroup.

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A. Umar, M. M. Zubairu. 2018-04-25. On certain semigroups of full contractions of a finite chain. https://arxiv.org/abs/1804.10057

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