An atomic MV-effect algebra with non-atomic center

Vladimír Olejček

Kybernetika (2007)

  • Volume: 43, Issue: 3, page 343-346
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Olejček, Vladimír. "An atomic MV-effect algebra with non-atomic center." Kybernetika 43.3 (2007): 343-346. <http://eudml.org/doc/33862>.

@article{Olejček2007,
abstract = {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.},
author = {Olejček, Vladimír},
journal = {Kybernetika},
keywords = {lattice effect algebra; MV-effect algebra; Archimedean effect algebra; sharp element; central element; atom; atomic MV-effect algebra; lattice effect algebra; sharp elements; central elements},
language = {eng},
number = {3},
pages = {343-346},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An atomic MV-effect algebra with non-atomic center},
url = {http://eudml.org/doc/33862},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Olejček, Vladimír
TI - An atomic MV-effect algebra with non-atomic center
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 3
SP - 343
EP - 346
AB - 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.
LA - eng
KW - lattice effect algebra; MV-effect algebra; Archimedean effect algebra; sharp element; central element; atom; atomic MV-effect algebra; lattice effect algebra; sharp elements; central elements
UR - http://eudml.org/doc/33862
ER -

References

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  2. Dvurečenskij A., Pulmannová S., New Trends in Quantum Structures Theory, Kluwer Academic Publications, Dordrecht 2000 MR1861369
  3. Foulis D. J., Bennett M. K., Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1325–1346 (1994) MR1304942
  4. Greechie R. J., Foulis, D., Pulmannová S., The center of an effect algebra, Order 12 (1995), 91–106 (1995) Zbl0846.03031MR1336539
  5. Jenča G., Riečanová Z., On sharp elements in lattice effect algebras, BUSEFAL 80 (1999), 24–29 (1999) 
  6. Kôpka F., Compatibility in D-posets, Internat. J. Theor. Phys. 34 (1995), 1525–1531 (1995) Zbl0851.03020MR1353696
  7. Kôpka F., Chovanec F., D-posets, Math. Slovaca 44 (1994), 21–34 (1994) MR1290269
  8. Riečanová Z., Continuous lattice effect algebras admitting order-continuous states, Fuzzy Sets and Systems 136 (2003), 41–54 MR1978468
  9. Riečanová Z., Archimedean atomic lattice effect algebras in which all sharp elements are central, Kybernetika 42 (2006), 2, 143–150 MR2241781
  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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