Results 81 to 90 of about 131 (121)
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Algebra Universalis, 1992
Let \({\mathcal C}(X)\) be the \(\perp\)-closed subsets of a set \(X\) with a binary relation \(\perp\) which is irreflexive, symmetric and satisfies \(x^{\perp\perp}=\{x\}\). For \(A,B\in{\mathcal C}(X)\) the relation \(A\theta B\) holds iff \([A\cap B,\;A\vee B]\) is of finite height.
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Let \({\mathcal C}(X)\) be the \(\perp\)-closed subsets of a set \(X\) with a binary relation \(\perp\) which is irreflexive, symmetric and satisfies \(x^{\perp\perp}=\{x\}\). For \(A,B\in{\mathcal C}(X)\) the relation \(A\theta B\) holds iff \([A\cap B,\;A\vee B]\) is of finite height.
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Orthomodular lattices as L-algebras
Soft Computing, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yali Wu, Yichuan Yang
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Decidability in Orthomodular Lattices
International Journal of Theoretical Physics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hyčko, Marek, Navara, Mirko
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Projective Orthomodular Lattices
Canadian Mathematical Bulletin, 1994AbstractWe introduce sectional projectivity, which appears to be the correct notion of projectivity when working with orthomodularlattices. We prove some positive results for varieties of OMLs satisfying various finiteness conditions, namely that every finite OML in such a variety is sectionally projective.
Bruns, Gunter, Roddy, Michael
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Varieties of Orthomodular Lattices
Canadian Journal of Mathematics, 1971In this paper we start investigating the lattice of varieties of orthomodular lattices. The varieties studied here are those generated by orthomodular lattices which are the horizontal sum of Boolean algebras. It turns out that these form a principal ideal in the lattice of all varieties of orthomodular lattices.
Bruns, Günter, Kalmbach, Gudrun
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Three Classes of Orthomodular Lattices
International Journal of Theoretical Physics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Greechie, Richard J., Legan, Bruce J.
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Projective orthomodular lattices II
Algebra Universalis, 1997The authors continue the study of projectivity in orthomodular lattices started in Part I [Can. Math. Bull. 37, No. 2, 145-153 (1994; Zbl 0819.06007)]. The main results: Theorem 1.1. No uncountable Boolean algebra is projective in the variety of all orthomodular lattices. Corollary 1.3. Every Boolean subalgebra of a free orthomodular lattice is at most
Bruns, G., Roddy, M. S.
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Conditional probabilities on orthomodular lattices
Reports on Mathematical Physics, 1984A definition of generalized probability on an orthomodular lattice which includes as particular cases the classical probability space and non- commutative probability theory on a von Neumann algebra is proposed. In this generalized structure the problem of conditioning with respect to Boolean \(\sigma\)-subalgebras is examined.
CASSINELLI, GIOVANNI, P. Truini:
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Orthomodular Lattices in Occurrence Nets
2009In this paper, we study partially ordered structures associated to occurrence nets. An occurrence net is endowed with a symmetric, but in general non transitive, concurrency relation. By applying known techniques in lattice theory, from any such relation one can derive a closure operator, and then an orthocomplemented lattice.
BERNARDINELLO, LUCA +2 more
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1990
The paper On complemented lattices was the third paper in the new theory of orthomodular lattices which started in 1936 with Birkhoff and von Neumann’s idea of developing a new many-valued logic for quantum mechanics by using the lattice of closed subspaces C(H) of a Hilbert space H as the valuation lattice.
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The paper On complemented lattices was the third paper in the new theory of orthomodular lattices which started in 1936 with Birkhoff and von Neumann’s idea of developing a new many-valued logic for quantum mechanics by using the lattice of closed subspaces C(H) of a Hilbert space H as the valuation lattice.
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