Factor congruences in BCK-algebras

In this paper, we characterize factor congruences in the quasivariety of BCK-algebras. As an application we prove that the free algebra over an infinite set of generators is indecomposable in any subvariety of BCK-algebras. We also study the decomposability of free algebras in the variety of hoop re...

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Detalles Bibliográficos
Autores: Abad, Manuel, Díaz Varela, José Patricio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/79644
Acceso en línea:http://hdl.handle.net/11336/79644
Access Level:acceso abierto
Palabra clave:Bck-Algebras
Decomposability
Factor Congruences
Free Algebras
Hoops
Implicative Filters
Pocrims
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:In this paper, we characterize factor congruences in the quasivariety of BCK-algebras. As an application we prove that the free algebra over an infinite set of generators is indecomposable in any subvariety of BCK-algebras. We also study the decomposability of free algebras in the variety of hoop residuation algebras (HBCK) and its subvarieties. We prove that free algebras in a non k-potent subvariety of HBCK are indecomposable while finitely generated free algebras in k-potent subvarieties have a unique non-trivial decomposition into a direct product of two factors, and one of them is the two-element implication algebra.