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arXiv · 1306.2774

On semigroups of endomorphisms of a chain with restricted range

Vítor H. Fernandes·Preeyanuch Honyam·Teresa M. Quinteiro·Boorapa Singha
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Abstract

Let $X$ be a finite or infinite chain and let $O(X)$ be the monoid of all endomorphisms of $X$. In this paper, we describe the largest regular subsemigroup of $O(X)$ and Green's relations on $O(X)$. In fact, more generally, if $Y$ is a nonempty subset of $X$ and $O(X,Y)$ the subsemigroup of $O(X)$ of all elements with range contained in $Y$, we characterize the largest regular subsemigroup of $O(X,Y)$ and Green's relations on $O(X,Y)$. Moreover, for finite chains, we determine when two semigroups of the type $O(X,Y)$ are isomorphic and calculate their ranks.

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Vítor H. Fernandes, Preeyanuch Honyam, Teresa M. Quinteiro, Boorapa Singha. 2013-06-12. On semigroups of endomorphisms of a chain with restricted range. https://arxiv.org/abs/1306.2774

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