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Eilenberg Theorems for Many-sorted Formations

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Eilenberg Theorems for Many-sorted Formations

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dc.contributor.author Climent Vidal, J.
dc.contributor.author Cosme i Llópez, Enric
dc.date.accessioned 2019-06-13T14:25:07Z
dc.date.available 2019-06-13T14:25:07Z
dc.date.issued 2019
dc.identifier.citation Climent Vidal, J. Cosme i Llópez, Enric 2019 Eilenberg Theorems for Many-sorted Formations Houston Journal of Mathematics 45 2 321 369
dc.identifier.uri https://hdl.handle.net/10550/70433
dc.description.abstract A theorem of Eilenberg establishes that there exists a bijectionbetween the set of all varieties of regular languages and the set of all vari-eties of finite monoids. In this article after defining, for a fixed set of sortsSand a fixedS-sorted signature Σ, the concepts of formation of congruenceswith respect to Σ and of formation of Σ-algebras, we prove that the alge-braic lattices of all Σ-congruence formations and of all Σ-algebra formationsare isomorphic, which is an Eilenberg's type theorem. Moreover, under asuitable condition on the free Σ-algebras and after defining the concepts offormation of congruences of finite index with respect to Σ, of formation offinite Σ-algebras, and of formation of regular languages with respect to Σ, weprove that the algebraic lattices of all Σ-finite index congruence formations,of all Σ-finite algebra formations, and of all Σ-regular language formationsare isomorphic, which is also an Eilenberg's type theorem.
dc.language.iso eng
dc.relation.ispartof Houston Journal of Mathematics, 2019, vol. 45, num. 2, p. 321-369
dc.subject Matemàtica
dc.subject Àlgebra
dc.title Eilenberg Theorems for Many-sorted Formations
dc.type journal article es_ES
dc.date.updated 2019-06-13T14:25:07Z
dc.identifier.idgrec 133244
dc.rights.accessRights open access es_ES

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