A Stone-Weierstrass theorem for MV-algebras and unital ℓ-groups

2013/12/29 by Leonardo Manuel Cabrer, Cabrer, L. M., Daniele Mundici +1
Computer Science · #06D35 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1312.7515

openalex publication_date 2013/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Working jointly in the equivalent categories of MV-al\-ge\-bras and lattice-ordered abelian groups with strong order unit (for short, unital ℓ-groups), we prove that isomorphism is a sufficient condition for a separating subalgebra A of a finitely presented algebra F to coincide with F. The separation and isomorphism conditions do not individually imply A=F. Various related problems, like the separation property of A, or A≅ F (for A a separating subalgebra of F), are shown to be (Turing-)decidable. We use tools from algebraic topology, category theory, polyhedral geometry and computational algebraic logic.

Citations

• The Euler characteristic of a polyhedron as a valuation on its coordinate vector lattice

Related

• Separable MV-algebras and lattice-groups
• On the Stone-Weierstrass theorem
• The Morita-equivalence between MV-algebras and abelian ℓ-groups with strong unit
• Simplicial geometry of unital lattice-ordered abelian groups
• Classification of finitely generated lattice-ordered abelian groups with order-unit