MATHEMATICA BOHEMICA, Vol. 126, No. 3, pp. 561-569 (2001)

A duality between algebras of basic logic and bounded representable $DRl$-monoids

Jiri Rachunek

Jiri Rachunek, Department of Algebra and Geometry, Faculty of Sciences, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: rachunek@risc.upol.cz

Abstract: $BL$-algebras, introduced by P. Hajek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that $BL$-algebras are the duals of bounded representable $DRl$-monoids. This duality enables us to describe some structure properties of $BL$-algebras.

Keywords: $BL$-algebra, $MV$-algebra, bounded $DRl$-monoid, representable $DRl$-monoid, prime spectrum

Classification (MSC2000): 06F05, 03B52, 03G20, 03G25

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