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.
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Received February 11, 2001; accepted in final form January 14, 2002.
RID="h1"
RID="h2"
ID="h1" Presented by W. Blok.
ID="h2" This paper was prepared while the first author was visiting the Universidad de Barcelona supported by INTERCAMPUS Program. The second author was partially supported by Grants SGR98/00018 of D.G.R. of Generalitat de Catalunya and PB 97-0888 of D.D.G.I.C.Y.T. of Spain.
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Cignoli, R., Torrens, A. Free algebras in varieties of BL-algebras with a Boolean retract.. Algebra univers. 48, 55–79 (2002). https://doi.org/10.1007/s00012-002-8204-1
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DOI: https://doi.org/10.1007/s00012-002-8204-1