Normalization of $MV$-algebras

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2005 Latin Publisher:Institute of Mathematics, Czech Academy of SciencesJournal:Mathematica Bohemica, volume 130, pages 283-300 (issn: 0862-7959, eissn: 2464-7136,

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Authors: Chajda, I.; Halaš, R.; Kühr, J.; Vanžurová, A.;

doi: 10.21136/mb.2005.134099

Normalization of $MV$-algebras

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Abstract

Summary: 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-algebras, abelian lattice-ordered group, Free algebras, normalization of a variety, $q$-lattice, Ordered abelian groups, Riesz groups, ordered linear spaces

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