Formations of finite monoids and formal languages: Eilenberg's variety theorem revisited
A. Ballester‐Bolinches, Jean-Éric Pin, Xaro Soler–Escrivà · Forum Mathematicum · 2012
Abstract 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.