Studia Logica

, Volume 89, Issue 1, pp 19–35

The Variety of Lattice Effect Algebras Generated by MV-algebras and the Horizontal Sum of Two 3-element Chains

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Abstract

It has been recently shown [4] that the lattice effect algebras can be treated as a subvariety of the variety of so-called basic algebras. The open problem whether all subdirectly irreducible distributive lattice effect algebras are just subdirectly irreducible MV-chains and the horizontal sum \({\mathcal{H}}\) of two 3-element chains is in the paper transferred into a more tractable one. We prove that modulo distributive lattice effect algebras, the variety generated by MV-algebras and \({\mathcal{H}}\) is definable by three simple identities and the problem now is to check if these identities are satisfied by all distributive lattice effect algebras or not.

Keywords

Lattice effect algebra basic algebra antitone involution variety 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Algebra and GeometryPalacký University OlomoucOlomoucCzech Republic

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