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Licensed Unlicensed Requires Authentication Published by De Gruyter June 19, 2012

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

Adolfo Ballester-Bolinches, Jean-Éric Pin and Xaro Soler-Escrivà
From the journal Forum Mathematicum


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.

MSC: 20D10; 20M35

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

Received: 2011-9-19
Revised: 2012-5-13
Published Online: 2012-6-19
Published in Print: 2014-11-1

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