**Financial support through the following projects:**

UIDB/00297/2020

UID/MAT/00297/2019

UID/MAT/00297/2013

PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

Title | On semigroups of orientation-preserving transformations with restricted range |

Publication Type | Journal Article |

Year of Publication | 2016 |

Authors | Fernandes VH, Honyam P, Quinteiro TM, Singha B |

Journal | Communications in Algebra |

Volume | 44 |

Pagination | 253-264 |

Abstract | Let $X_n$ be a chain with n elements ($nın\N$) and let $ØP_n$ be the monoid of all orientation-preserving transformations of $X_n$. In this paper, for any nonempty subset $Y$ of $X_n$, we consider the subsemigroup $ØP_n(Y)$ of $ØP_n$ of all transformations with range contained in $Y$: we describe the largest regular subsemigroup of $ØP_n(Y)$, which actually coincides with its subset of all regular elements, and Green’s relations on $ØP_n(Y)$. Also, we determine when two semigroups of the type $ØP_n(Y)$ are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid $ØR_n$ of all either orientation-preserving or orientation-reversing transformations of $X_n$. |

URL | http://www.tandfonline.com/doi/pdf/10.1080/00927872.2014.975345 |

DOI | 10.1080/00927872.2014.975345 |