Notes on divisible MV-algebras

TL;DR

This paper explores divisible MV-algebras, linking them to rational vector lattices, and establishes dualities and categorical structures to deepen understanding of their algebraic and geometric properties.

Contribution

It introduces a categorical adjunction for divisible hulls and proves a duality between finitely presented algebras and rational polyhedra, advancing the theory of MV-algebras.

Findings

Connected divisible MV-algebras with $\\mathbb{Q}$-vector lattices

Presented a categorical adjunction for divisible hulls

Proved a duality between finitely presented algebras and rational polyhedra

Abstract

In these notes we study the class of divisible MV-algebras inside the algebraic hierarchy of MV-algebras with product. We connect divisible MV-algebras with $\mathbb Q$-vector lattices, we present the divisible hull as a categorical adjunction and we prove a duality between finitely presented algebras and rational polyhedra.