MATHEMATICA BOHEMICA, Vol. 123, No. 4, pp. 437-441 (1998)

MV-algebras are categorically equivalent to a class of $\Cal{DR}l_1(i)$-semigroups

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: In the paper it is proved that the category of \MV-algebras is equivalent to the category of bounded \DRl-semigroups satisfying the identity $1-(1-x)=x$. Consequently, by a result of D. Mundici, both categories are equivalent to the category of bounded commutative \BCK-algebras.

Keywords: \MV-algebra, \DRl-semigroup, categorical equivalence, bounded \BCK-algebra

Classification (MSC2000): 06F05, 06D30, 06F35

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