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arXiv · 0902.0297

Free adequate semigroups

Mark Kambites
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Abstract

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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Mark Kambites. 2009-05-08. Free adequate semigroups. https://arxiv.org/abs/0902.0297

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