Riesz space-valued states on pseudo MV-algebras

2017/09/19 by Anatolij Dvurečenskij, Dvurečenskij, Anatolij
Computer Science · Decision Sciences · #06C15 #06D35 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1709.06502

openalex publication_date 2017/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce Riesz space-valued states, called (R,1_R)-states, on a pseudo MV-algebra, where R is a Riesz space with a fixed strong unit 1_R. Pseudo MV-algebras are a non-commutative generalization of MV-algebras. Such a Riesz space-valued state is a generalization of usual states on MV-algebras. Any (R,1_R)-state is an additive mapping preserving a partial addition in pseudo MV-algebras. Besides we introduce (R,1_R)-state-morphisms and extremal (R,1_R)-states, and we study relations between them. We study metrical completion of unital ℓ-groups with respect to an (R,1_R)-state. If the unital Riesz space is Dedekind complete, we study when the space of (R,1_R)-states is a Choquet simplex or even a Bauer simplex.

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