Abstract
We introduce a notion of commutativity inquantum MV-algebras (QMV-algebras) and we investigatethe corresponding structure of the center. It turns outthat the center of a QMV-algebra is a multivalued algebra (MV-algebra). Finally, we prove thatthe center of the QMV-algebra of all effects on aHilbert space is irreducible.
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REFERENCES
Chang, C. C. (1957). Algebraic analysis of many valued logics, Transactions of the American Mathematical Society, 88, 74–80.
Chang, C. C. (1958). A new proof of the completeness of Lukasiewicz axioms, Transactions of the American Mathematical Society, 93, 467–490.
Giuntini, R. (1995a). Quasilinear QMV algebras, International Journal of Theoretical Physics, 34, 397–1407.
Giuntini, R. (1995b). Unsharp orthoalgebras and quantum MV algebras, in The Foundations of Quantum Mechanics— Historical Analysis and Open Questions, C. Garola and A. Rossi, eds., Kluwer, Dordrecht, pp. 325–337.
Giuntini, R. (1996). Quantum MV algebras, Studia Logica, 56, 393–417.
Giuntini, R., and Greuling, H. (1989). Toward an unsharp language for unsharp properties, Foundations of Physics, 19, 931–945.
Kalmbach, G. (1983). Orthomodular Lattices, Academic Press, New York.
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Giuntini, R. Quantum MV-Algebras and Commutativity. International Journal of Theoretical Physics 37, 65–74 (1998). https://doi.org/10.1023/A:1026609121718
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DOI: https://doi.org/10.1023/A:1026609121718