### Abstract

The aim of this paper is to develop the calculus of trivializers for subsemigroups.

Given a finite presentation P defining a semigroup S and a trivializer of the Squier

complex of P, we obtain an infinite trivializer of the Squier complex of a finite

presentation defining a subsemigroup of S. Also, we give a method to find finite

trivializers for special subsemigroups and hence to show that those subsemigroups

have finite derivation type (FDT). An application of this method is given: we prove

that if S = B[Y, Sα] is a band of monoids having FDT, then so does Sα, for any

α ∈ Y .

Given a finite presentation P defining a semigroup S and a trivializer of the Squier

complex of P, we obtain an infinite trivializer of the Squier complex of a finite

presentation defining a subsemigroup of S. Also, we give a method to find finite

trivializers for special subsemigroups and hence to show that those subsemigroups

have finite derivation type (FDT). An application of this method is given: we prove

that if S = B[Y, Sα] is a band of monoids having FDT, then so does Sα, for any

α ∈ Y .

Original language | English |
---|---|

Title of host publication | Semigroups and formal languages. Proceedings of the international conference in honour of the 65th birthday of Donald B. McAlister |

Pages | 188-204 |

Number of pages | 17 |

Publication status | Published - 6 Jul 2007 |

Event | International Conference on Semigroups and Languages in honour of the 65th birthday of Donald B. McAlister - Duration: 1 Jan 2005 → … |

### Conference

Conference | International Conference on Semigroups and Languages in honour of the 65th birthday of Donald B. McAlister |
---|---|

Period | 1/01/05 → … |

## Fingerprint Dive into the research topics of 'On trivializers and Subsemigroups'. Together they form a unique fingerprint.

## Cite this

Malheiro, A. J. M. D. C. M. (2007). On trivializers and Subsemigroups. In

*Semigroups and formal languages. Proceedings of the international conference in honour of the 65th birthday of Donald B. McAlister*(pp. 188-204)