Holoïdes factoriels - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Studia Scientiarum Mathematicarum Hungarica Année : 1977

Holoïdes factoriels


An "holoid" is a commutative monoid in which division is a partial order. Dubreil, Fuchs, Mitsch and Bosbach studied certain holoids in which every element has a unique factorization (possibly reduced) into irreducible, prime or maxiaml elements. We give a specific meaning to the words "reduction" and "reduced". Then we study a new family of holoids, called factorial -- a concept which generalizes the previous holoids with "unique factorization" --. The most meaningful difference is that we don't suppose any chain condition. However, we have again the "good" properties of these holoids: existence of l.c.m., existence of a minimum solution to the equation ax = b when a divides b. We also prove the following result: if H is factorial, then it is also factorial with respect of l.c.m. as a law of composition.

Mots clés

Fichier principal
Vignette du fichier
Holoides.pdf (204.49 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00017719 , version 1 (17-09-2016)


  • HAL Id : hal-00017719 , version 1


Jean-Eric Pin. Holoïdes factoriels. Studia Scientiarum Mathematicarum Hungarica, 1977, 12, pp.169-184. ⟨hal-00017719⟩


216 Consultations
42 Téléchargements


Gmail Facebook X LinkedIn More