Boolean carried homomorphisms in orthomodular lattices

• Autorzy: Matousek M.
• Języki publikacji: EN

Abstrakty

EN

Let L, L1 be orthomodular lattices. Let us say that a surjective homomorphism f : L - L1 is Boolean carried if for any maximal Boolean subalgebra B1 of L1 there is a maximal Boolean subalgebra B of L such that f(B) = B1. In this note we investigate the class HOMC all L's such that all surjective homomorphisms from L to orthomodular lattices are Boolean carried. We prove as a main result that if L possesses at most countably many infinite maximal Boolean subalgebras then L L HOMC- We also relate the class HOMCto the classes previously studied and provide some model-theoretic propertiesHOMC.

Słowa kluczowe

EN

Boolean algebra; homomorphism; orthomodular lattice; axiomatizable class

PL

algebra Boole'a; homomorfizm; kraty

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 2
• Strony: 255--265
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Matousek M.

• Department of Logic, Philosophical Faculty of the Charles University, Celetná 20, 116 42 Prague 1, Czech Republic

Bibliografia

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• [11] G. Kalmbach, Orthomodular Lattices, Academic Press, London, 1983.
• [12] P. Pták, S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer Academic Publishers, Dordrecht/Boston/London, 1991.