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We study $\mathbb H$-perfect pseudo MV-algebras, that is, algebras which canbe split into a system of ordered slices indexed by the elements of an subgroup$\mathbb H$ of the group of the real numbers. We show when they can berepresented as a lexicographic product of $\mathbb H$ with some $\ell$-group.In addition, we show also a categorical equivalence of this category with thecategory of $\ell$-groups.

$\mathbb H$-perfect Pseudo MV-algebras and Their Representations