Abstract
Our main result is stating and proving a necessary and sufficient condition forD-poset and effect algebras to have MacNeille completions.
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REFERENCES
Birkhoff, G., Lattice Theory, AMS, Providence, Rhode Island, 1967.
G. Bruns R. Greechie, J. Harding, and M. Roddy, Completions of orthomodular lattices, Order 7 (1990), 67-76.
Foulis, D., and Bennett, M. K., Effect algebras and unsharp quantum logic, Found. Phys. 24 (1994), 1331-1352.
Greechie, R. J., Foulis, D., and Pulmannovä, S., The center of an effect algebra, Order 12 (1995), 91-106.
Gudder, S. P., D-algebras, Found. Phys. 26 (1994), 813-822.
Harding, J., Completions of orthomodular lattice II, Order 10 (1993), 283-294.
Kalmbach, G., Orthomodular lattices, Academic Press, London, 1983.
Kôpka, F., D-posets of fuzzy sets, Tatra Mt. Math. Publ. 1 (1992), 83-87.
Kôpka, F., and Chovanec, F., D-posets, Math. Slovaca 44 (1994), 21-34.
Pulmannovä, S., and Rie?anovä, Z., Compact topological orthomodular lattices, Contrib. Gen. Algebra 7 (1991), 277-283.
Riečanovä, Z., Applications of topological methods to the completion of atomic orthomodular lattices, Demonstratio Math. XXIV (1991), 332-339.
Riečanovä Z., Topological and order-topological orthomodular lattices, Bull. Aust. Math. Soc. 47 (1993), 509-518.
Riečanovä, Z., On order continuity of quantum structures and their homomorphisms, Demonstratio Math. 29 (1996), 433-443.
Riečanovä, Z., On proper orthoalgebras, difference posets and abelian relative inverse semigroup, Tatra Mountains Math. Publ. 10 (1997), 119-128.
Riečanovä, Z., Subalgebras, intervals and central elements of generalized effect algebras (1998), Int. J. Theor. Physics 38 (1999), 3209-3220.
Schmidt, J., Zur Kennzeichnung der Dedekind-Mac Neilleschen Hulle einer Geordneten Menge, Arch. Math. 7 (1956), 241-249.
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Riečkanov´, Z. MacNeille Completions of D-Posets and Effect Algebras. International Journal of Theoretical Physics 39, 859–869 (2000). https://doi.org/10.1023/A:1003683014627
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DOI: https://doi.org/10.1023/A:1003683014627