Relevant bibliographies by topics / Orthomodular lattices

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Academic literature on the topic 'Orthomodular lattices'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Orthomodular lattices"

1

Riecanová, Zdenka. "Topological and order-topological orthomodular lattices." Bulletin of the Australian Mathematical Society 46, no. 3 (1992): 509–18. http://dx.doi.org/10.1017/s0004972700012168.

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The necessary and sufficient conditions for atomic orthomodular lattices to have the MacNeille completion modular, or (o)-continuous or order topological, orthomodular lattices are proved. Moreover we show that if in an orthomodular lattice the (o)-convergence of filters is topological then the (o)-convergence of nets need not be topological. Finally we show that even in the case when the MacNeille completion of an orthomodular lattice L is order-topological, then in general the (o)-convergence of nets in does not imply their (o)-convergence in L. (This disproves, also for the orthomodular and
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2

Chajda, Ivan, and Helmut Länger. "Left residuated lattices induced by lattices with a unary operation." Soft Computing 24, no. 2 (2019): 723–29. http://dx.doi.org/10.1007/s00500-019-04461-x.

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Abstract In a previous paper, the authors defined two binary term operations in orthomodular lattices such that an orthomodular lattice can be organized by means of them into a left residuated lattice. It is a natural question if these operations serve in this way also for more general lattices than the orthomodular ones. In our present paper, we involve two conditions formulated as simple identities in two variables under which this is really the case. Hence, we obtain a variety of lattices with a unary operation which contains exactly those lattices with a unary operation which can be conver
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3

Chajda, Ivan, and Helmut Länger. "Weakly orthomodular and dually weakly orthomodular posets." Asian-European Journal of Mathematics 11, no. 02 (2018): 1850093. http://dx.doi.org/10.1142/s1793557118500936.

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Orthomodular posets form an algebraic semantic for the logic of quantum mechanics. We show several methods how to construct orthomodular posets via a representation within the powerset of a given set. Further, we generalize this concept to the concept of weakly orthomodular and dually weakly orthomodular posets where the complementation need not be antitone or an involution. We show several interesting examples of such posets and prove which intervals of these posets are weakly orthomodular or dually weakly orthomodular again. To every (dually) weakly orthomodular poset can be assigned an alge
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Mikhaeel, Nabila N., and Basim Samir Labib. "States and Boolean Algebra." Algebra Colloquium 15, no. 04 (2008): 649–52. http://dx.doi.org/10.1142/s1005386708000618.

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We investigate subadditive measures on orthomodular lattices. We show as the main result that the Boolean algebra, the special metric orthomodular lattice and the orthomodular lattice which is unital with respect to subadditive states are equivalent. This result may find an application in the foundation of quantum theories and mathematical logic.
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Dai, Songsong. "Rough Approximation Operators on a Complete Orthomodular Lattice." Axioms 10, no. 3 (2021): 164. http://dx.doi.org/10.3390/axioms10030164.

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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 distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.
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Kermani, Neda Arjomand, Esfandiar Eslami, and Arsham Borumand Saeid. "Central lifting property for orthomodular lattices." Mathematica Slovaca 70, no. 6 (2020): 1307–16. http://dx.doi.org/10.1515/ms-2017-0433.

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AbstractWe introduce and investigate central lifting property (CLP) for orthomodular lattices as a property whereby all central elements can be lifted modulo every p-ideal. It is shown that prime ideals, maximal ideals and finite p-ideals have CLP. Also Boolean algebras, simple chain finite orthomodular lattices, subalgebras of an orthomodular lattices generated by two elements and finite orthomodular lattices have CLP. The main results of the present paper include the investigation of CLP for principal p-ideals and finite direct products of orthomodular lattices.
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7

Bruns, Gunter, and Michael Roddy. "Projective Orthomodular Lattices." Canadian Mathematical Bulletin 37, no. 2 (1994): 145–53. http://dx.doi.org/10.4153/cmb-1994-021-2.

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AbstractWe 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. In contrast, we prove that the eight element modular ortholattice, MO 3, is not projective in the variety of modular ortholattices.
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8

Hedlı́ková, Jarmila. "Relatively orthomodular lattices." Discrete Mathematics 234, no. 1-3 (2001): 17–38. http://dx.doi.org/10.1016/s0012-365x(00)00189-8.

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9

Choe, Tae Ho, and Richard J. Greechie. "Profinite orthomodular lattices." Proceedings of the American Mathematical Society 118, no. 4 (1993): 1053. http://dx.doi.org/10.1090/s0002-9939-1993-1143016-9.

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10

Carrega, J. C. "Minimal orthomodular lattices." International Journal of Theoretical Physics 34, no. 8 (1995): 1265–70. http://dx.doi.org/10.1007/bf00676237.

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Books on the topic "Orthomodular lattices"

1

Beran, Ladislav. Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7.

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Beran, Ladislav. Orthomodular Lattices: Algebraic Approach. Springer Netherlands, 1985.

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Orthomodular lattices: Algebraic approach. D. Reidel, 1985.

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Measures and Hilbert lattices. World Scientific, 1986.

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5

Kalmbach, Gudrun. Quantum measures and spaces. Kluwer, 1998.

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Kalmbach, G. Quantum measures and spaces. Kluwer, 1998.

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7

1939-, Pulmannová Sylvia, ed. Orthomodular structures as quantum logics. Kluwer Academic Publishers, 1991.

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8

Pták, Pavel, and Sylvia Pulmannová. Orthomodular Structures as Quantum Logics: Intrinsic Properties, State Space and Probabilistic Topics (Fundamental Theories of Physics). Springer, 1991.

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Book chapters on the topic "Orthomodular lattices"

1

Beran, Ladislav. "Introduction." In Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7_1.

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Beran, Ladislav. "Elementary Theory of Orthomodular Lattices." In Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7_2.

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Beran, Ladislav. "Structure of Orthomodular Lattices." In Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7_3.

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Beran, Ladislav. "Amalgams." In Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7_4.

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Beran, Ladislav. "Generalized Orthomodular Lattices." In Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7_5.

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Beran, Ladislav. "Solvability of Generalized Orthomodular Lattices." In Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7_6.

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Beran, Ladislav. "Special Properties of Orthomodularity." In Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7_7.

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Beran, Ladislav. "Application." In Orthomodular Lattices. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5215-7_8.

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Kalmbach, Gudrun. "On Orthomodular Lattices." In The Dilworth Theorems. Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4899-3558-8_9.

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Bernardinello, Luca, Lucia Pomello, and Stefania Rombolà. "Orthomodular Lattices in Occurrence Nets." In Applications and Theory of Petri Nets. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02424-5_11.

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Conference papers on the topic "Orthomodular lattices"

1

Florek, Jan. "Orthomodular lattices and closure operations in ordered vector spaces." In Noncommutative Harmonic Analysis with Applications to Probability II. Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc89-0-7.

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Dankel II, D. D., R. V. Rodriguez, and F. D. Anger. "HAIM OMLET: An Expert System For Research In Orthomodular Lattices And Related Structures." In 1986 Technical Symposium Southeast, edited by John F. Gilmore. SPIE, 1986. http://dx.doi.org/10.1117/12.964115.

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