Tensor products and the Loomis-Sikorski theorem for MV-algebras

DOI10.1006/aama.1998.0631zbMath0926.06004OpenAlexW1989551546MaRDI QIDQ1291066

Publication date: 21 November 1999

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aama.1998.0631

zbMATH Keywords

tribe MV-algebras maximal ideals semisimple algebras generalization of the Loomis-Sikorski theorem MV-tensor product

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) MV-algebras (06D35) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (65)

Effect algebras with state operator ⋮ Sharp and unsharp observables on \(\sigma \)-MV algebras -- a comparison with the Hilbert space approach ⋮ Franco Montagna's work on provability logic and many-valued logic ⋮ Every state on semisimple MV-algebra is integral ⋮ Remarks on effect-tribes ⋮ Hahn-Banach theorems for MV-algebras ⋮ Smearing of observables and spectral measures on quantum structures ⋮ Equational type characterization for \(\sigma\)-complete MV-algebras. ⋮ Compatibility of observables on effect algebras ⋮ \(n\)-dimensional observables on \(k\)-perfect MV-algebras and \(k\)-perfect effect algebras. I: Characteristic points ⋮ Topological properties of prime filters in MTL-algebras and fuzzy set representations for MTL-algebras ⋮ An analysis of the logic of Riesz spaces with strong unit ⋮ Two-dimensional observables and spectral resolutions ⋮ Scalar extensions for algebraic structures of Łukasiewicz logic. ⋮ Sharp and fuzzy observables on effect algebras ⋮ Quasi product on Boolean D-posets ⋮ MV-modules ⋮ An algebraic generalization of the notion of tribe ⋮ Polyhedral MV-algebras ⋮ Markov kernels and tribes ⋮ Observables on quantum structures ⋮ Notes on divisible MV-algebras ⋮ Boolean algebras of conditionals, probability and logic ⋮ MV-algebras with operators (the commutative and the non-commutative case). ⋮ A logical characterization of coherence for imprecise probabilities ⋮ Some remarks on divisible polyhedral MV-algebras ⋮ On two versions of the Loomis-Sikorski theorem for algebraic structures ⋮ Unnamed Item ⋮ Representable effect algebras and observables ⋮ Coherence of the Product Law for Independent Continuous Events ⋮ ON THE LOOMIS–SIKORSKI THEOREM FOR MV-ALGEBRAS WITH INTERNAL STATE ⋮ A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra ⋮ Unnamed Item ⋮ Ł\(\Pi\) logic with fixed points ⋮ Olson order of quantum observables ⋮ Topology on the set of \(R_{0}\) semantics for \(R_{0}\) algebras ⋮ Operations that preserve integrability, and truncated Riesz spaces ⋮ MV-algebras with internal states and probabilistic fuzzy logics ⋮ Non-reversible betting games on fuzzy events: complexity and algebra ⋮ Conditional probability on MV-algebras ⋮ Representation and extension of states on MV-algebras ⋮ Loomis-Sikorski representation of monotone \(\sigma\)-complete effect algebras ⋮ MV-observables and MV-algebras ⋮ On the entropy of dynamical systems in product MV algebras ⋮ Rota's Fubini lectures: the first problem ⋮ \(\bigstar\)-autonomous lattices and fuzzy sets ⋮ Adding structure to MV-algebras ⋮ Kolmogorov-Sinaj entropy on MV-algebras ⋮ Quantum observables and effect algebras ⋮ On the semisimple tensor product of MV-algebras ⋮ Representations of pseudo Vitali spaces and Loomis–Sikorski theorem ⋮ Fuzzy topology representation for MV-algebras ⋮ Loomis-Sikorski theorem for monotone σ-complete effect algebras ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Betting on continuous independent events ⋮ Unnamed Item ⋮ State-morphism MV-algebras ⋮ Lifting, \(n\)-dimensional spectral resolutions, and \(n\)-dimensional observables ⋮ Conditional probability on \(\sigma\)-MV-algebras ⋮ Observables on perfect MV-algebras ⋮ Spectral resolutions in Dedekind \(\sigma\)-complete \(\ell\)-groups ⋮ THE LOOMIS–SIKORSKI THEOREM FOR -ALGEBRAS ⋮ ON THE SUM OF OBSERVABLES IN PRODUCT MV ALGEBRAS ⋮ State BCK-algebras and state-morphism BCK-algebras.

Cites Work

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