Artículo
Implicit definition of the quaternary discriminator
Fecha de publicación:
10/2012
Editorial:
Birkhauser Verlag Ag
Revista:
Algebra Universalis
ISSN:
0002-5240
e-ISSN:
1420-8911
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let A be an algebra. A function f: A n → A is implicitly definable by a system of term equations Λ t i(x i,...,x n,z)if f is the only n-ary operation on A making the identities t i(x,f(x))≈ s i(x,f(x)) hold in A. Let K be a class of non-trivial algebras. We prove that the quaternary discriminator is implicitly definable on every member of K (via the same system) iff K is contained in the class of relatively simple members of some relatively semisimple quasivariety with equationally definable relative principal congruences. As an application, we obtain a characterization of the relatively permutable members of such type of quasivarieties. Furthermore, we prove that every algebra in such a quasivariety has a unique relatively permutable extension. © 2012 Springer Basel AG.
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Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Campercholi, Miguel Alejandro Carlos; Vaggione, Diego Jose; Implicit definition of the quaternary discriminator; Birkhauser Verlag Ag; Algebra Universalis; 68; 1-2; 10-2012; 1-16
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