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Abstract:

The aim of this paper is to give a description of the free algebras in varieties of BL-algebras having the Boolean retraction property. This description is given in terms of weak Boolean products over Cantor spaces. The stalks are obtained in a constructive way from free radical algebras. Radical algebras are obtained endowing the maximal radicals of BL-algebras with a unary operation corresponding to double negation. The radical algebras obtained from a variety of BL-algebras form themselves a variety, that in the cases of PL-algebras and bipartite MV-algebras can be identified with the class of cancellative hoops.

Registro:

Documento: Artículo
Título:Free algebras in varieties of BL-algebras with a Boolean retract
Autor:Cignoli, R.; Torrens, A.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires - CONICET, 1428 Buenos Aires, Argentina
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Palabras clave:BL-algebras; Boolean representation; Boolean retraction property; Free BL-algebras; Peirce representation; Radical algebras; Radical variety
Año:2002
Volumen:48
Número:1
Página de inicio:55
Página de fin:79
DOI: http://dx.doi.org/10.1007/s00012-002-8204-1
Título revista:Algebra Universalis
Título revista abreviado:Algebra Univers.
ISSN:00025240
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00025240_v48_n1_p55_Cignoli

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Citas:

---------- APA ----------
Cignoli, R. & Torrens, A. (2002) . Free algebras in varieties of BL-algebras with a Boolean retract. Algebra Universalis, 48(1), 55-79.
http://dx.doi.org/10.1007/s00012-002-8204-1
---------- CHICAGO ----------
Cignoli, R., Torrens, A. "Free algebras in varieties of BL-algebras with a Boolean retract" . Algebra Universalis 48, no. 1 (2002) : 55-79.
http://dx.doi.org/10.1007/s00012-002-8204-1
---------- MLA ----------
Cignoli, R., Torrens, A. "Free algebras in varieties of BL-algebras with a Boolean retract" . Algebra Universalis, vol. 48, no. 1, 2002, pp. 55-79.
http://dx.doi.org/10.1007/s00012-002-8204-1
---------- VANCOUVER ----------
Cignoli, R., Torrens, A. Free algebras in varieties of BL-algebras with a Boolean retract. Algebra Univers. 2002;48(1):55-79.
http://dx.doi.org/10.1007/s00012-002-8204-1