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Normal filters in residuated lattices. (English) Zbl 1326.03081

Summary: Residuated lattices play an important role in the study of fuzzy logic. In the present paper, we introduce the notion of a normal filter in a residuated lattice and give some characterizations of them. We state and prove some theorems and examples which determine the relationship between this notion and the other types of filters of a residuated lattice. Finally we investigate the relation between the set of dense elements and normal filters of a residuated lattice.

MSC:

03G25 Other algebras related to logic
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