Free algebras in varieties of BL-algebras with a Boolean retract

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 al...

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Autores principales: Cignoli, R., Torrens, A.
Formato: JOUR
Materias:
BL-algebras
Boolean representation
Boolean retraction property
Free BL-algebras
Peirce representation
Radical algebras
Radical variety
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00025240_v48_n1_p55_Cignoli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00025240_v48_n1_p55_Cignoli
record_format dspace
spelling todo:paper_00025240_v48_n1_p55_Cignoli2023-10-03T13:52:25Z Free algebras in varieties of BL-algebras with a Boolean retract Cignoli, R. Torrens, A. BL-algebras Boolean representation Boolean retraction property Free BL-algebras Peirce representation Radical algebras Radical variety 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00025240_v48_n1_p55_Cignoli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic BL-algebras
Boolean representation
Boolean retraction property
Free BL-algebras
Peirce representation
Radical algebras
Radical variety
spellingShingle BL-algebras
Boolean representation
Boolean retraction property
Free BL-algebras
Peirce representation
Radical algebras
Radical variety
Cignoli, R.
Torrens, A.
Free algebras in varieties of BL-algebras with a Boolean retract
topic_facet BL-algebras
Boolean representation
Boolean retraction property
Free BL-algebras
Peirce representation
Radical algebras
Radical variety
description 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.
format JOUR
author Cignoli, R.
Torrens, A.
author_facet Cignoli, R.
Torrens, A.
author_sort Cignoli, R.
title Free algebras in varieties of BL-algebras with a Boolean retract
title_short Free algebras in varieties of BL-algebras with a Boolean retract
title_full Free algebras in varieties of BL-algebras with a Boolean retract
title_fullStr Free algebras in varieties of BL-algebras with a Boolean retract
title_full_unstemmed Free algebras in varieties of BL-algebras with a Boolean retract
title_sort free algebras in varieties of bl-algebras with a boolean retract
url http://hdl.handle.net/20.500.12110/paper_00025240_v48_n1_p55_Cignoli
work_keys_str_mv AT cignolir freealgebrasinvarietiesofblalgebraswithabooleanretract
AT torrensa freealgebrasinvarietiesofblalgebraswithabooleanretract
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