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A short equational axiomatization of orthomodular lattices.
, 1976 Bolesław Sobociński
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A complete and countable orthomodular lattice is atomic [PDF]
, 1969 C. H. Randall
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Categorical Equivalence Between Orthomodular Dynamic Algebras and Complete Orthomodular Lattices
, 2017 Kohei Kishida +3 more
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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.
Günter Bruns, Michael S. Roddy
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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.
Günter Bruns, Gudrun Kalmbach
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Boolean quotients of orthomodular lattices [PDF]
Algebra Universalis, 1995 Let \(L\) be an orthomodular lattice and \(J\) a proper \(p\)-ideal of \(L\) (i.e. a lattice ideal such that \(a \in L\), \(b \in L \Rightarrow (a \vee b') \wedge b \in L)\). The present paper investigates the properties of those orthomodular lattices for which there exist nontrivial Boolean quotients \(L/J\).
Sylvia Pulmannová, A. B. D'Andrea
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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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Completions of orthomodular lattices
Order, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
John Harding +3 more
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A Note on Orthomodular Lattices
International Journal of Theoretical Physics, 2016We introduce a new identity equivalent to the orthomodular law in every ortholattice.
Bonzio S., Chajda I.
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