Archive for Mathematical Logic 40 (6):467-473 (2001)

Abstract
BL-algebras rise as Lindenbaum algebras from many valued logic introduced by Hájek [2]. In this paper Boolean ds and implicative ds of BL-algebras are defined and studied. The following is proved to be equivalent: (i) a ds D is implicative, (ii) D is Boolean, (iii) L/D is a Boolean algebra. Moreover, a BL-algebra L contains a proper Boolean ds iff L is bipartite. Local BL-algebras, too, are characterized. These results generalize some theorems presented in [4], [5], [6] for MV-algebras which are BL-algebras fulfiling an additional double negation law x = x **
Keywords Key words or phrases: Many-valued logic – Fuzzy logic –MV-algebra –BL-algebra – Residuated lattice
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DOI 10.1007/s001530100088
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Hyper-Archimedean BL-Algebras Are MV-Algebras.Esko Turunen - 2007 - Mathematical Logic Quarterly 53 (2):170-175.
N -Fold Filters in BL-Algebras.Masoud Haveshki & Esfandiar Eslami - 2008 - Mathematical Logic Quarterly 54 (2):176-186.

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