## Abstract

A semigroup S is called left ample if it can be embedded in the symmetric inverse semigroup I_{X} of partial bijections of a non-empty set X such that the image of S is closed under the unary operation α ↦−→ αα^{−1}, where α^{−1} is the inverse of α in I_{X}. Right ample semigroups are defined dually. A semigroup is called ample if it is both left and right ample. A monoid is (left, right) ample if it is (left, right) ample as a semigroup. We observe that the dominion of an ample subsemigroup of I_{X} coincides with the inverse subsemigroup of I_{X} generated by it. We then determine the dominions of certain submonoids of I_{n}, the symmetric inverse semigroup over a finite chain 1 < 2 < · · · < n.

Original language | British English |
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Pages (from-to) | 17-28 |

Number of pages | 12 |

Journal | Acta et Commentationes Universitatis Tartuensis de Mathematica |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - 30 May 2023 |

## Keywords

- Ample monoid
- dominion
- epimorphism
- symmetric inverse semigroup over a finite chain