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

TL;DR

This paper investigates $ ext{ extbf{H}}$-perfect pseudo MV-algebras, exploring their structure, representation as lexicographic products, and establishing a categorical equivalence with $ ext{ extbf{l}}$-groups, advancing the algebraic understanding of these structures.

Contribution

It characterizes $ ext{ extbf{H}}$-perfect pseudo MV-algebras and proves their representation as lexicographic products, also establishing a categorical equivalence with $ ext{ extbf{l}}$-groups.

Findings

Characterization of $ ext{ extbf{H}}$-perfect pseudo MV-algebras.

Representation as lexicographic products with $ ext{ extbf{l}}$-groups.

Categorical equivalence between the categories of these algebras and $ ext{ extbf{l}}$-groups.

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.