On direct decompositions of certain orthomodular lattices.
Konôpka, P., Pulmannová, S. (1991)
Acta Mathematica Universitatis Comenianae. New Series
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Displaying similar documents to “Ring-like structures derived from $\lambda $-lattices with antitone involutions”
On direct decompositions of certain orthomodular lattices.
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A measure-theoretic characterization of Boolean algebras among orthomodular lattices
Pavel Pták, Sylvia Pulmannová (1994)
Commentationes Mathematicae Universitatis Carolinae
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We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures. This result may find an application in the foundation of quantum theories, mathematical logic, or elsewhere.
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The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the...