Lexicographic pseudo effect algebras

DOI10.1007/s00500-016-2228-5zbMath1420.03146OpenAlexW2460473013MaRDI QIDQ1701973

Anatolij Dvurečenskij

Publication date: 27 February 2018

Published in: Soft Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00500-016-2228-5

zbMATH Keywords

effect algebrapo-groupstrong unitlexicographic productpseudo effect algebraretractive ideallexicographic ideal\((H,u)\)-perfect effect algebraantilatticelexicographic effect algebrastrongly \((H,u)\)-perfect effect algebrathe Riesz decomposition property

Mathematics Subject Classification ID

Complemented lattices, orthocomplemented lattices and posets (06C15) Quantum logic (03G12) Ordered groups (06F15)

Cites Work

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• Effect algebras and unsharp quantum logics.
• Observations on non-commutative fuzzy logic
• Lexicographic pseudo MV-algebras
• Gödel spaces and perfect MV-algebras
• Coproduct MV-algebras, nonstandard reals, and Riesz spaces
• Perfect MV-algebras are categorically equivalent to Abelian \(l\)-groups
• Lexicographic MV-algebras and lexicographic states.
• Riesz decomposition properties and the lexicographic product of po-groups
• Lexicographic effect algebras
• The logic of quantum mechanics
• Perfect effect algebras are categorically equivalent with Abelian interpolation po-groups
• A non-commutative generalization of MV-algebras
• Pseudo MV-algebras are intervals in ℓ-groups
• Compatibility and decompositions of effects
• Pseudoeffect algebras. I: Basic properties
• Pseudoeffect algebras. II: Group representations

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