On semigroups of endomorphisms of a chain with restricted range

Vítor H. Fernandes, Preeyanuch Honyam, Teresa M. Quinteiro, Boorapa Singha

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9 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)77-104
Number of pages28
JournalSemigroup Forum
Volume89
Issue number1
DOIs
Publication statusPublished - 1 Aug 2014

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Keywords

  • Order-preserving
  • Rank
  • Restricted range
  • Transformations

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