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FREE ADEQUATE SEMIGROUPS

Part of: Semigroups Algebraic structures

Published online by Cambridge University Press:  19 March 2012

MARK KAMBITES
MARK KAMBITES*
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK (email: [email protected])
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Abstract

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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.

Keywords

adequate semigroupfree objectword problemMunn tree

MSC classification

Secondary: 20M10: General structure theory 08A50: Word problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 3 , December 2011 , pp. 365 - 390
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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