Lexicographic Pseudo MV-algebras

2015/06/10 by Dvurečenskij, Anatolij
#03G12 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1506.03188

Abstract

A lexicographic pseudo MV-algebra is an algebra that is isomorphic to an interval in the lexicographic product of a linear unital group with an arbitrary ℓ-group. We present conditions when a pseudo MV-algebra is lexicographic. We show that a key condition is the existence of a lexicographic ideal, or equivalently, a case when the algebra can be split into comparable slices indexed by elements of the interval [0,u] of some unital linearly ordered group (H,u). Finally, we show that fixing (H,u), the category of (H,u)-lexicographic pseudo MV-algebras is categorically equivalent to the category of ℓ-groups.

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