## Abstract

Proper extensions that are "injective on a"'-related idempotents" of a">-unipotent semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a lambda-semidirect product of a left regular band by an a">-unipotent or by a glrac semigroup, respectively. An example of such is the generalized Szendrei expansion.

As a consequence of our embedding, we are able to give a structure theorem for proper left restriction semigroups. Further, we show that any glrac semigroup S has a proper cover that is a semidirect product of a left regular band by a monoid, and if S is left restriction, the left regular band may be taken to be a semilattice.

Original language | English |
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Pages (from-to) | 51-70 |

Number of pages | 20 |

Journal | Semigroup forum |

Volume | 81 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 2010 |

## Keywords

- Expansions
- R-unipotent semigroups
- Generalised restriction
- LEFT AMPLE SEMIGROUPS
- UNIPOTENT SEMIGROUP
- INVERSE-SEMIGROUPS
- EXPANSION
- MONOIDS