Results 11 to 20 of about 1,603 (177)
An Intrisic Topology for Orthomodular Lattices [PDF]
International Journal of Theoretical Physics, 2007 We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space.
A. Wilce +15 more
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Residuation in orthomodular lattices
Topological Algebra and its Applications, 2017 We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness.
Chajda Ivan, Länger Helmut
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Implication connectives in orthomodular lattices. [PDF]
Notre Dame Journal of Formal Logic, 1975 Louis Herman +2 more
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Modular pairs in orthomodular lattices [PDF]
Pacific Journal of Mathematics, 1966 Erik A. Schreiner
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Orthogonality and complementation in the lattice of subspaces of a finite vector space [PDF]
Mathematica Bohemica, 2022 We investigate the lattice $ L( V)$ of subspaces of an $m$-dimensional vector space $ V$ over a finite field ${\rm GF}(q)$ with a prime power $q=p^n$ together with the unary operation of orthogonality.
Ivan Chajda, Helmut Länger
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Non-commutative symmetric differences in orthomodular lattices [PDF]
International Journal of Theoretical Physics, 2002 We deal with the following question: What is the proper way to introduce symmetric difference in orthomodular lattices? Imposing two natural conditions on this operation, six possibilities remain: the two (commutative) normal forms of the symmetric difference in Boolean algebras and four non-commutative terms. It turns out that in many respects the non-
Gerhard Dorfer
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On locally finite orthomodular lattices [PDF]
Mathematica Slovaca, 2022 Abstract Let us denote by ℒ ℱ $[\mathcal{L}\mathcal{F}$ the ...
Dominika Burešová, Pavel Pták
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Rough Approximation Operators on a Complete Orthomodular Lattice
Axioms, 2021 This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the
Songsong Dai
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The paraunitary group of a von Neumann algebra
Bulletin of the London Mathematical Society, Volume 54, Issue 4, Page 1220-1231, August 2022., 2022 Abstract It is proved that the pure paraunitary group over a von Neumann algebra coincides with the structure group of its projection lattice. The structure group of an arbitrary orthomodular lattice (OML) is a group with a right invariant lattice order, and as such it is known to be a complete invariant of the OML.
Carsten Dietzel, Wolfgang Rump
wiley +1 more source
Cyclic atoms in orthomodular lattices [PDF]
Proceedings of the American Mathematical Society, 1971 Let P ( H ) P(H) denote the projection lattice of a separable Hilbert space H. For each x ∈ H {\text {x}} \in H , let P x {P_{\text {x}}} denote the projection onto the one ...
Donald E. Catlin
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