### 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) |
---|---|

Pages (from-to) | 1-55 |

Number of pages | 55 |

Journal | Journal of Pure and Applied Algebra |

Volume | 34 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1984 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

}

*Journal of Pure and Applied Algebra*, vol. 34, no. 1, pp. 1-55. https://doi.org/10.1016/0022-4049(84)90055-0

**Iteration of expansions - unambiguous semigroups.** / Birget, Jean-Camille.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Iteration of expansions - unambiguous semigroups

AU - Birget, Jean-Camille

PY - 1984/1/1

Y1 - 1984/1/1

N2 - 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 ŜL, resp. ŜR, 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).

AB - 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 ŜL, resp. ŜR, 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).

UR - http://www.scopus.com/inward/record.url?scp=0002819566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002819566&partnerID=8YFLogxK

U2 - 10.1016/0022-4049(84)90055-0

DO - 10.1016/0022-4049(84)90055-0

M3 - Article

AN - SCOPUS:0002819566

VL - 34

SP - 1

EP - 55

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1

ER -