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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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