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

Abstract

We study $\mathbb{H}$-perfect pseudo MV-algebras, that is, algebras which can be 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 be represented as a lexicographic product of $\mathbb{H}$ with some $\ell$-group. In addition, we show also a categorical equivalence of this category with the category of $\ell$-groups.