### Abstract

New expansions for global semigroup theory are developed. Many expansions have a left and a right version, each with specific (dual) properties; e.g., the Rhodes expansions Ŝ^{L}, resp. Ŝ^{R}, have unambiguous L-resp. R-order. In applications one sometimes needs expansions having both properties simultaneously; these can be constructed by alternately applying the left and the right expansion (possibly infinitely often) while keeping the same set of generators. Thus one obtains an expansion which is invariant under application of the old two expansions and thus has the properties of both (e.g., one obtains -+ with {A figure is presented}, and so -+ has unambiguous L-and R-order). It is proved that, in the case of the Rhodes expansion, the new expansion is 'close' to the original semigroup; in particular (and this is the main result of the paper), Ŝ^{+}_{A} is finite (resp. finite J-above) if S is finite (resp. finiteJ-above).

Original language | English (US) |
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Pages (from-to) | 1-55 |

Number of pages | 55 |

Journal | Journal of Pure and Applied Algebra |

Volume | 34 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1984 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory