MATHEMATICA BOHEMICA, Vol. 130, No. 3, pp. 283-300 (2005)

Normalization of $MV$-algebras

I. Chajda, R. Halas, J. Kühr, A. Vanzurova

I. Chajda, R. Halas, J. Kühr, A. Vanzurova, Dept. of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

Abstract: We consider algebras determined by all normal identities of $MV$-algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a $q$-lattice, and another one based on a normalization of a lattice-ordered group.

Keywords: $MV$-algebra, abelian lattice-ordered group, $q$-lattice, normalization of a variety

Classification (MSC2000): 06D35, 06D05, 06F20, 08B20

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