## Abstract

An ordered pair (e,f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent. Previously [1] we have established that there are four distinct types of skew pairs of idempotents. We have also described (as quotient semigroups of certain regular Rees matrix semigroups [2]) the structure of the smallest regular semigroups that contain precisely one skew pair of each of the four types, there being to within isomorphism ten such semigroups. These we call the derived Rees matrix semigroups. In the particular case of full transformation semigroups we proved in [3] that T_{X} contains all four skew pairs of idempotents if and only if |X| ≥ 6. Here we prove that T_{X} contains all ten derived Rees matrix semigroups if and only if |X| ≥ 7.

Original language | English |
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Pages (from-to) | 219-233 |

Number of pages | 15 |

Journal | Semigroup Forum |

Volume | 73 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 2006 |

## Keywords

- Regular Semigroup
- Semigroup Forum
- Transformation Semigroup
- Rees Matrix Semigroup
- Dual Isomorphism