### 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)

### Cite this

**On the semigroups of partial one-to-one order-decreasing finite transformations.** / Umar, Abdullahi.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*, vol. 123, no. 2, pp. 355-363. https://doi.org/10.1017/S0308210500025737

}

TY - JOUR

T1 - On the semigroups of partial one-to-one order-decreasing finite transformations

AU - Umar, Abdullahi

PY - 1993

Y1 - 1993

N2 - Let In be the symmetric inverse semigroup on Xn = {1,…,n}, let SIn be the subsemigroup of strictly partial one-to-one self-maps of Xn and let [formula-omitted] be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of Xn. 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 Jn-1.

AB - Let In be the symmetric inverse semigroup on Xn = {1,…,n}, let SIn be the subsemigroup of strictly partial one-to-one self-maps of Xn and let [formula-omitted] be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of Xn. 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 Jn-1.

UR - http://www.scopus.com/inward/record.url?scp=84972102836&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972102836&partnerID=8YFLogxK

U2 - 10.1017/S0308210500025737

DO - 10.1017/S0308210500025737

M3 - Article

AN - SCOPUS:84972102836

VL - 123

SP - 355

EP - 363

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -