The Riesz hull of a semisimple MV-algebra

TL;DR

This paper introduces the Riesz hull construction for semisimple MV-algebras, extending the concept of vector-lattice hulls from lattice-ordered groups to the setting of MV-algebras, enriching their algebraic structure.

Contribution

It defines the Riesz hull for semisimple MV-algebras, bridging the gap between MV-algebras and Riesz spaces through a novel categorical construction.

Findings

Riesz hull of a semisimple MV-algebra is well-defined.

Establishes categorical equivalence with Riesz spaces.

Provides a new tool for analyzing MV-algebras.

Abstract

MV-algebras and Riesz MV-algebras are categorically equivalent to abelian lattice-ordered groups with strong unit and, respectively, with Riesz spaces (vector-lattices) with strong unit. A standard construction in the literature of lattice-ordered groups is the vector-lattice hull of an archimedean lattice-ordered group. Following a similar approach, in this paper we define the Riesz hull of a semisimple MV-algebra.