BL-algebras rise as Lindenbaum algebras from many valued logic introduced b
y Hajek [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) LID 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 pr
esented in [4], [5], [6] for MV-algebras which are BL-algebras fulfiling an
additional double negation law x = x**.