Ordered monoids and J-trivial monoids

Karsten Henckell (1) , Jean-Eric Pin (2)

1 NEW COLLEGE OF FLORIDA - New College of Florida
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

The aim of this paper is to give a new proof of the following result of Straubing and Thérien (which is also a consequence of a well-known result of I. Simon): Every J-trivial monoid is a quotient of an ordered monoid satisfying the identity x <= 1. We give a proof of this result which provides a direct construction of the covering ordered monoid.

Mots clés: semigroup; monoid; ordered semigroup; J-trivial

Domaines: Autre [cs.OH]; Théorie des groupes [math.GR]

Karsten Henckell, Jean-Eric Pin. Ordered monoids and J-trivial monoids. J.-C. Birget, S. Margolis, J. Meakin and M. Sapir. Algorithmic problems in Groups and Semigroups (Lincoln, NE, 1998), Birkhäusern, Boston, MA, USA, pp.121-137, 2000, Trends in Mathematics. ⟨hal-00112620⟩