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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.
Wydawca
Czasopismo
Rocznik
Tom
Strony
255--265
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Department of Logic, Philosophical Faculty of the Charles University, Celetná 20, 116 42 Prague 1, Czech Republic
Bibliografia
- [1] L. Beran, Orthomodular Lattices, Algebraic Approach, D. Reidel, Dordrecht, 1985.
- [2] G. Bruns, R. Greechie, Blocks and commutators in orthomodular lattices, Algebra Universalis 27 (1990), 1-9.
- [3] G. Bruns, J. Harding, Algebraic aspects of orthomodular lattices, in: B. Coecke, D. Moore and A. Wilce (eds.), Current Research in Operational Quantum Logic, 2000, 37-65.
- [4] G. Bruns, M. Roddy, Projective orthomodular lattices, Canad. Math. Bull. 37 (2) (1994), 145-153.
- [5] G. Bruns, M. Roddy, Projective orthomodular lattices II, Algebra Universalis 37 (1997), 143-153.
- [6] S. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York Inc., 1973.
- [7] C. C. Chang, H. J. Keisler, Model Theory, North-Holland Publishing Company, Amsterdam, London, 1973.
- [8] G. Chevalier, Commutators and decompositions of orthomodular lattices, Order 6 (1989), 181-194.
- [9] A. B. d 'Andrea, S. Pulmannová, Boolean quotiens of orthomodular lattices, Algebra Universalis 34 (1995), 485-495.
- [10] J. Harding, Lectures on Orthomodular Lattices, Prague 1997.
- [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-PWA3-0010-0002