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Small varieties of finite semigroups and extensions

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Jean-Eric Pin ,
Howard Straubing  and
Denis Therien
Jean-Eric Pin
Affiliation:
Université ParisVI et C.N.R.S. Laboratorie d'Informatique Théorique Tour 55–65 4 Place Jussieu 75230 Paris Cedex 05, France
Howard Straubing
Affiliation:
Department of Mathematics Reed CollegePortland, OregonU.S.A.97202
Denis Therien
Affiliation:
School of Computer Science McGill UniversityMontréal Québec, H3A 2K6, Canada
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Abstract

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We find the atoms of certain subclasses of varieties of finite semigroups and the corresponding varieties of languages. For example we give a new description of languages whose syntactic monoids are R-trivial and idempotent. We also describe the least variety containing all commutative semigroups and at least one non-commutative semigroup. Finally we extend to varieties of finite semigroups some classical results about semilattice decomposition of semigroups.

MSC classification

Secondary: 20M35: Semigroups in automata theory, linguistics, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 269 - 281
Copyright
Copyright © Australian Mathematical Society 1984

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