, Volume 89, Issue 1, pp 19-35
Date: 28 May 2008

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.

Presented by Daniele Mundici