FREE ADEQUATE SEMIGROUPS

The word problem for free adequate semigroups

We study the complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids. We present polynomial time (quadratic in the RAM model of computation) algorithms to solve the word problem and compute normal forms in each of these, and hence also to test whether any given identity holds in the classes of left, right and/or two-sided adequate semigroups.

Retracts of Trees and Free Left Adequate Semigroups

Recent research of the author has studied edge-labelled directed trees under a natural multiplication operation. The class of all such trees (with a fixed labelling alphabet) has an algebraic interpretation, as a free object in the class of adequate semigroups. We consider here a natural subclass of these trees, defined by placing a restriction on edge orientations, and show that the resulting ...

FREE SEMIGROUPS AND IDEMPOTENTS IN T

The known theory for an oid T shows how to find a subset T of ?T, which is a compact right topological semigroup [I]. The success of the methods in [2] for obtaining properties of-T has prompted us to see how successful they would be in another context. Thus we find (Theorem 4.8) that T cont ains copies of free semigroups on 2? generators, is an immediate consequence of the stronger resu...

Free Burnside Semigroups

Uniformities on Free Semigroups

Résumé. On sait que les complétions profinies d’un semigroupe libre qui sont associées à une pseudovariété de semigroupes ou de semigroupes ordonnés peuvent être définies par un écart ou un quasi-écart. Nous caractérisons les quasi-écarts et les quasi-uniformités qui peuvent être obtenues de cette façon. Nous démontrons également l’existence d’une correspondance injective “à la Eilenberg”, entr...