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Pseudo BL-algebras and \(\text{DR}\ell\)-monoids. (English) Zbl 1024.06005
Summary: It is shown that pseudo BL-algebras are categorically equivalent to certain bounded DR\(\ell\)-monoids. Using this result, we obtain some properties of pseudo BL-algebras, in particular, we can characterize congruence kernels by means of normal filters. Further, we deal with representable pseudo BL-algebras and, in conclusion, we prove that they form a variety.

MSC:
06D35 MV-algebras
06F05 Ordered semigroups and monoids
03G25 Other algebras related to logic
03B52 Fuzzy logic; logic of vagueness
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