### Abstract

Let In be the symmetric inverse semigroup on X_{n} = {1,…,n}, let SI_{n} be the subsemigroup of strictly partial one-to-one self-maps of X_{n} and let [formula-omitted] be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of X_{n}. In this paper it is shown that In is an (irregular, for n ≥ 2) type A semigroup with n D-classes and d=g Further, it is shown that In- is generated by the n(n + 1)/2 quasi-idempotents in J_{n-1}.

Original language | English |
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Pages (from-to) | 355-363 |

Number of pages | 9 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 123 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1993 |

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### ASJC Scopus subject areas

- Mathematics(all)