### Abstract

An ordered regular semigroup S is E-special if for every x ∈ S there is a biggest x ^{+} ∈ S such that both xx ^{+} and x ^{+} x are idempotent. Every regular strong Dubreil–Jacotin semigroup is E-special, as is every ordered completely simple semigroup with biggest inverses. In an E-special ordered regular semigroup S in which the unary operation x → x ^{+} is antitone the subset P of perfect elements is a regular ideal, the biggest inverses in which form an inverse transversal of P if and only if S has a biggest idempotent. If S ^{+} is a subsemigroup and S does not have a biggest idempotent, then P contains a copy of the crown bootlace semigroup.

Original language | English |
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Pages (from-to) | 3294-3312 |

Number of pages | 19 |

Journal | Communications in Algebra |

Volume | 43 |

Issue number | 8 |

DOIs | |

Publication status | Published - 3 Aug 2015 |

### Keywords

- Crown bootlace semigroup
- Dubreil–Jacotin semigroup
- E-special
- Inverse transversal

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## Cite this

Blyth, T. S., & Santos, M. H. A. (2015). E-special Ordered Regular Semigroups.

*Communications in Algebra*,*43*(8), 3294-3312. https://doi.org/10.1080/00927872.2014.918987