A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Defect theorems with compatibility relations
Tekijät: Halava V, Harju T, Kärki T
Kustantaja: SPRINGER
Julkaisuvuosi: 2008
Journal: Semigroup Forum
Tietokannassa oleva lehden nimi: SEMIGROUP FORUM
Lehden akronyymi: SEMIGROUP FORUM
Vuosikerta: 76
Numero: 1
Aloitussivu: 1
Lopetussivu: 24
Sivujen määrä: 24
ISSN: 0037-1912
DOI: https://doi.org/10.1007/s00233-007-9013-9
Tiivistelmä
We consider words together with a compatibility relation induced by a relation on letters. Unique factorization with respect to two arbitrary word relations R and S defines the (R,S)-freeness of the semigroup considered. We generalize the stability theorem of Schutzenberger and Tilson's closure result for (R,S)-free semigroups. The inner and the outer (R,S)-unique factorization hull and the (R,S)-free hull of a set of words are introduced and we show how they can be computed. We prove that the (R,S)-unique factorization hulls possess a defect effect, which implies a variant of a cumulative defect theorem of word semigroups. In addition, a defect theorem of partial words is proved as a corollary.
We consider words together with a compatibility relation induced by a relation on letters. Unique factorization with respect to two arbitrary word relations R and S defines the (R,S)-freeness of the semigroup considered. We generalize the stability theorem of Schutzenberger and Tilson's closure result for (R,S)-free semigroups. The inner and the outer (R,S)-unique factorization hull and the (R,S)-free hull of a set of words are introduced and we show how they can be computed. We prove that the (R,S)-unique factorization hulls possess a defect effect, which implies a variant of a cumulative defect theorem of word semigroups. In addition, a defect theorem of partial words is proved as a corollary.
Turun yliopiston Tutkimustietojärjestelmän portaali