MATHEMATICA BOHEMICA, Vol. 128, No. 2, pp. 199-208 (2003)

Pseudo $BL$-algebras and $DR\ell$-monoids

Jan Kühr

Jan Kühr, Department of Algebra and Geometry, Faculty of Sciences, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: kuhr@inf.upol.cz

Abstract: 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.

Keywords: pseudo $BL$-algebra, $DR\ell$-monoid, filter, polar, representable pseudo $BL$-algebra

Classification (MSC2000): 06F05, 03G25

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