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lattice effect algebra; MV-effect algebra; Archimedean effect algebra; sharp element; central element; atom
Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.
[1] Chang C. C.: Algebraic analysis of many-valued logics. Trans. Amer. Math. Math. Soc. 88 (1958), 467–490 MR 0094302 | Zbl 0084.00704
[2] Dvurečenskij A., Pulmannová S.: New Trends in Quantum Structures Theory. Kluwer Academic Publications, Dordrecht 2000 MR 1861369
[3] Foulis D. J., Bennett M. K.: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1325–1346 MR 1304942
[4] Greechie R. J., Foulis, D., Pulmannová S.: The center of an effect algebra. Order 12 (1995), 91–106 MR 1336539 | Zbl 0846.03031
[5] Jenča G., Riečanová Z.: On sharp elements in lattice effect algebras. BUSEFAL 80 (1999), 24–29
[6] Kôpka F.: Compatibility in D-posets. Internat. J. Theor. Phys. 34 (1995), 1525–1531 MR 1353696 | Zbl 0851.03020
[7] Kôpka F., Chovanec F.: D-posets. Math. Slovaca 44 (1994), 21–34 MR 1290269
[8] Riečanová Z.: Continuous lattice effect algebras admitting order-continuous states. Fuzzy Sets and Systems 136 (2003), 41–54 MR 1978468
[9] Riečanová Z.: Archimedean atomic lattice effect algebras in which all sharp elements are central. Kybernetika 42 (2006), 2, 143–150 MR 2241781
[10] Riečanová Z., Marinová, I., Zajac M.: Some aspects of generalized prelattice effect algebras. In: Theory and Application of Relational Structures as Knowledge Instruments II (H. de Swart et al., eds., Lecture Notes in Artificial Intelligence 4342), Springer–Verlag, Berlin 2006, pp. 290–317
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