Free adequate semigroups

Details Free adequate semigroups Free adequate semigroups

2009-02-02

arxiv.org/abs/0902.0297v3

Mathematics

Rings and Algebras

24 pages, 3 figures, references added, typos fixed, some proofs shortened, results unchanged

Scientific paper

We give an explicit description of the free objects in the quasivariety of adequate semigroups, as sets of labelled directed trees under a natural combinatorial multiplication. The morphisms of the free adequate semigroup onto the free ample semigroup and into the free inverse semigroup are realised by a combinatorial "folding" operation which transforms our trees into Munn trees. We use these results to show that free adequate semigroups and monoids are J-trivial and never finitely generated as semigroups, and that those which are finitely generated as (2,1,1)-algebras have decidable word problem.

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