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Forum Mathematicum

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Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 26, Issue 6


Formations of finite monoids and formal languages: Eilenberg's variety theorem revisited

Adolfo Ballester-Bolinches
  • Departament d'Àlgebra, Universitat de València, C/ Dr. Moliner, 50 46100-Burjassot (València), Spain
  • Other articles by this author:
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/ Jean-Éric Pin / Xaro Soler-Escrivà
  • Dpt. d'Estadística i Investigació Operativa, Universitat d'Alacant, Sant Vicent del Raspeig, Ap. Correus 99, E-03080 Alacant, Spain
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Published Online: 2012-06-19 | DOI: https://doi.org/10.1515/forum-2012-0055


We present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.

Keywords: Group formations; regular languages; semigroups; automata theory

MSC: 20D10; 20M35

About the article

Received: 2011-09-19

Revised: 2012-05-13

Published Online: 2012-06-19

Published in Print: 2014-11-01

Funding Source: MICINN (Spain)

Award identifier / Grant number: Proyecto MTM2010-19938-C03-01

Funding Source: ANR 2010 BLAN 0202 02 FREC

Funding Source: Universitat Politècnica de València

Award identifier / Grant number: PAID-02-09

Citation Information: Forum Mathematicum, Volume 26, Issue 6, Pages 1737–1761, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0055.

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