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.
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
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