Distributive atomic efect algebras

• Autorzy: Riečanová Z.
• Języki publikacji: EN

Abstrakty

EN

Motivated by the use of fuzzy or unsharp quantum logics as carriers of probability measures there have been recently introduced effect algebras (D-posets). We extend a result by Greechie, Foulis and Pulmannova of finite distributive effect algebras to all Archimedean atomic distributive effect algebras. We show that every such an effect algebra is join and meet dense in a complete effect algebra being a direct product of finite chains and distributive diamonds. This proves that every such effect algebra has a MacNeille completion being again a distributive effect algebra and both these effect algebras are continuous lattices. Moreover, we show that every faithful or (o)-continuous state (probability) on such an effect algebra is a valuation, hence a subadditive state. Its existence is also proved. Finally, we prove that every complete atomic distributive effect algebra E is a homomorphic image of a complete modular atomic ortholattice regarded as effect algebra and E is an MV-effect algebra (MV-algebra) if and only if it is a homomorphic image of a Boolean algebra regarded as effect algebra.

Słowa kluczowe

EN

MV-algebras; MacNeille completions; valuations

PL

MV-algebra

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 2
• Strony: 247--259
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Riečanová Z.

• Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 812 19 Bratislava 1, Slovak Republic

Bibliografia

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