Pseudo MV-algebras and Lexicographic Product
Anatolij Dvure\v{c}enskij

TL;DR
This paper explores algebraic conditions under which pseudo MV-algebras can be represented as intervals in lexicographic products of specific lattice-ordered groups, establishing categorical equivalences.
Contribution
It introduces $(H,u)$-perfect and strong $(H,u)$-perfect pseudo MV-algebras and provides a representation theorem linking them to lexicographic products.
Findings
Characterization of pseudo MV-algebras as lexicographic intervals
Introduction of $(H,u)$-perfect pseudo MV-algebras
Categorical equivalence between strong $(H,u)$-perfect pseudo MV-algebras and $ ext{l}$-groups
Abstract
We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital -group and an -group that is not necessary Abelian. We introduce -perfect pseudo MV-algebras and strong -perfect pseudo MV-algebras, the latter ones will have a representation by a lexicographic product. Fixing a unital -group , the category of strong -perfect pseudo MV-algebras is categorically equivalent to the category of -groups.
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