Pseudo MV-algebras and Lexicographic Product

2014/06/09 by Dvurečenskij, Anatolij
#03G20 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1406.2339

Abstract

We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital ℓ-group and an ℓ-group that is not necessary Abelian. We introduce (H,u)-perfect pseudo MV-algebras and strong (H,u)-perfect pseudo MV-algebras, the latter ones will have a representation by a lexicographic product. Fixing a unital ℓ-group (H,u), the category of strong (H,u)-perfect pseudo MV-algebras is categorically equivalent to the category of ℓ-groups.

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• Lexicographic Pseudo MV-algebras
• \mathbb H-perfect Pseudo MV-algebras and Their Representations
• Lexicographic Effect Algebras
• Lexicographic Product vs \mathbb Q-perfect and \mathbb H-perfect Pseudo Effect Algebras
• Some results on pseudo MV-algebras with square roots