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Orthomodular Lattices
, 2008
"... Summary. The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example ..."
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of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings – as a relational structure (poset) and as a lattice. As a preliminary work, we present the proofs of the dependence of other axiomatizations of ortholattices. The formalization of the properties of orthomodular lattices
OF A N ORTHOMODULAR LATTICE
"... On the Lebesgue decomposition of a function relative to a pideal of an orthomodular lattice ..."
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On the Lebesgue decomposition of a function relative to a pideal of an orthomodular lattice
Orthomodular Lattices and Quantales
, 2008
"... Abstract. Let L be a complete orthomodular lattice. There is a one to one correspondence between complete boolean subalgebras of L contained in the center of L and endomorphisms j of L satisfying the BorceuxVan den Bossche conditions. ..."
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Cited by 2 (0 self)
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Abstract. Let L be a complete orthomodular lattice. There is a one to one correspondence between complete boolean subalgebras of L contained in the center of L and endomorphisms j of L satisfying the BorceuxVan den Bossche conditions.
Implications and equivalences in orthomodular lattices
"... A graphical method for evaluating expressions in orthomodular lattices introduced by M. Navara in [3] is extended to a method for checking the validity of classical logic implications and equvivalences of identities with two variables. We present possible extensions of the presented method for the ..."
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A graphical method for evaluating expressions in orthomodular lattices introduced by M. Navara in [3] is extended to a method for checking the validity of classical logic implications and equvivalences of identities with two variables. We present possible extensions of the presented method
On Interval Homogeneous Orthomodular Lattices
"... An orthomodular lattice L is said to be interval homogeneous (resp. centrally interval homogeneous) if it is oecomplete and satisfies the following property: Whenever L is isomorphic to an interval, [a; b], in L then L is isomorphic to each interval [c; d] with c a and d b (resp. the same con ..."
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Cited by 5 (2 self)
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An orthomodular lattice L is said to be interval homogeneous (resp. centrally interval homogeneous) if it is oecomplete and satisfies the following property: Whenever L is isomorphic to an interval, [a; b], in L then L is isomorphic to each interval [c; d] with c a and d b (resp. the same
An Intrisic Topology for Orthomodular Lattices
, 2008
"... 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. Moreover, we show that in the case of a boolean algebra, the obtained topology is the ..."
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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. Moreover, we show that in the case of a boolean algebra, the obtained topology
Profinite orthomodular lattices
 Proceedings of the American Mathematical Society
, 1993
"... Abstract. If X is a variety of orthomodular lattices generated by a finite orthomodular lattice the MacNeille completion of every algebra in X again belongs to X. AMS subject classilkatioo (1980). 06xX Key words. Orthomodular lattice, variety of algebras, MacNeille completion. The MacNeille complet ..."
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Cited by 10 (2 self)
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Abstract. If X is a variety of orthomodular lattices generated by a finite orthomodular lattice the MacNeille completion of every algebra in X again belongs to X. AMS subject classilkatioo (1980). 06xX Key words. Orthomodular lattice, variety of algebras, MacNeille completion. The Mac
On Quantic Conuclei in Orthomodular Lattices
, 1996
"... . In this paper we study the lattice of conuclei for orthomodular lattices. We show that under certain conditions we can get a complete characterization of all quantic conuclei. The thing to note is that we use a noncommutative, nonassociative disjunction operator which can be thought of as from n ..."
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Cited by 3 (0 self)
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. In this paper we study the lattice of conuclei for orthomodular lattices. We show that under certain conditions we can get a complete characterization of all quantic conuclei. The thing to note is that we use a noncommutative, nonassociative disjunction operator which can be thought of as from
ON SOLVABILITY OF GENERALIZED ORTHOMODULAR LATTICES
"... The purpose of this paper is to establish a universal criterion for a generalized orthomodular lattice to belong to a primitive class of lattices. The starting point for the investigation is the description of the reflection and the coreflection. These lattices can be determined bytwo lattice cong ..."
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The purpose of this paper is to establish a universal criterion for a generalized orthomodular lattice to belong to a primitive class of lattices. The starting point for the investigation is the description of the reflection and the coreflection. These lattices can be determined bytwo lattice
Orthomodular Lattices and a Quantum Algebra
 Int. J. Theor. Phys
, 2001
"... Abstract. We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is embeddable into the algebra. To obtain this result w ..."
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Cited by 6 (4 self)
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Abstract. We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is embeddable into the algebra. To obtain this result
Results 1  10
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745