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An orthomodular lattice admitting no group-valued measure


Author: Mirko Navara
Journal: Proc. Amer. Math. Soc. 122 (1994), 7-12
MSC: Primary 06C15; Secondary 03G12, 28B10
DOI: https://doi.org/10.1090/S0002-9939-1994-1191871-X
MathSciNet review: 1191871
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Abstract: We construct a finite orthomodular lattice L such that, for each commutative group G, there is no nontrivial G-valued measure on L. This result extends a result of R. J. Greechie (Orthogonal lattices admitting no states, J. Combin. Theory Ser. A 10 (1971), 119-132), and also sheds light on recent investigations in the noncommutative measure theory.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1191871-X
Keywords: Orthomodular lattice, group-valued measure, Greechie diagram
Article copyright: © Copyright 1994 American Mathematical Society

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