Archimedean atomic lattice effect algebras in which all sharp elements are central

Zdena Riečanová

Kybernetika (2006)

  • Volume: 42, Issue: 2, page 143-150
  • ISSN: 0023-5954

Abstract

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We prove that every Archimedean atomic lattice effect algebra the center of which coincides with the set of all sharp elements is isomorphic to a subdirect product of horizontal sums of finite chains, and conversely. We show that every such effect algebra can be densely embedded into a complete effect algebra (its MacNeille completion) and that there exists an order continuous state on it.

How to cite

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Riečanová, Zdena. "Archimedean atomic lattice effect algebras in which all sharp elements are central." Kybernetika 42.2 (2006): 143-150. <http://eudml.org/doc/33797>.

@article{Riečanová2006,
abstract = {We prove that every Archimedean atomic lattice effect algebra the center of which coincides with the set of all sharp elements is isomorphic to a subdirect product of horizontal sums of finite chains, and conversely. We show that every such effect algebra can be densely embedded into a complete effect algebra (its MacNeille completion) and that there exists an order continuous state on it.},
author = {Riečanová, Zdena},
journal = {Kybernetika},
keywords = {lattice effect algebra; sharp and central element; block; state; subdirect decomposition; MacNeille completion; lattice effect algebra; sharp element; central element; block; subdirect decomposition; MacNeille completion},
language = {eng},
number = {2},
pages = {143-150},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Archimedean atomic lattice effect algebras in which all sharp elements are central},
url = {http://eudml.org/doc/33797},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Riečanová, Zdena
TI - Archimedean atomic lattice effect algebras in which all sharp elements are central
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 2
SP - 143
EP - 150
AB - We prove that every Archimedean atomic lattice effect algebra the center of which coincides with the set of all sharp elements is isomorphic to a subdirect product of horizontal sums of finite chains, and conversely. We show that every such effect algebra can be densely embedded into a complete effect algebra (its MacNeille completion) and that there exists an order continuous state on it.
LA - eng
KW - lattice effect algebra; sharp and central element; block; state; subdirect decomposition; MacNeille completion; lattice effect algebra; sharp element; central element; block; subdirect decomposition; MacNeille completion
UR - http://eudml.org/doc/33797
ER -

References

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  1. Chang C. C., 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490 (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
  2. Dvurečenskij A., Pulmannová S., New Trends in Quantum Structures, Kluwer Academic Publishers, Dordrecht – Boston – London and Ister Science, Bratislava 2000 MR1861369
  3. Foulis D., Bennett M. K., 10.1007/BF02283036, Found. Phys. 24 (1994), 1331–1352 (1994) MR1304942DOI10.1007/BF02283036
  4. Greechie R. J., 10.1016/0097-3165(71)90015-X, J. Combin. Theory Ser. A 10 (1971), 119–132 (1971) Zbl0219.06007MR0274355DOI10.1016/0097-3165(71)90015-X
  5. Greechie R. J., Foulis, D., Pulmannová S., 10.1007/BF01108592, Order 12 (1995), 91–106 (1995) Zbl0846.03031MR1336539DOI10.1007/BF01108592
  6. Jenča G., Riečanová Z., On sharp elements in lattice effect algebras, BUSEFAL 80 (1999), 24–29 (1999) 
  7. Kôpka F., Chovanec F., D -posets, Math. Slovaca 44 (1994), 21–34 (1994) Zbl0789.03048MR1290269
  8. Riečanová Z., 10.1023/A:1003683014627, Internat. J. Theor. Phys. 39 (2000), 859–869 Zbl0967.06008MR1792204DOI10.1023/A:1003683014627
  9. Riečanová Z., 10.1023/A:1003619806024, Internat. J. Theor. Phys. 39 (2000), 231–237 Zbl0968.81003MR1762594DOI10.1023/A:1003619806024
  10. Riečanová Z., Archimedean and block-finite lattice effect algebras, Demonstratio Math. 33 (2000), 443–452 MR1791464
  11. Riečanová Z., Orthogonal sets in effect algebras, Demonstratio Math. 34 (2001), 3, 525–532 MR1853730
  12. Riečanová Z., 10.1023/A:1011911512416, Internat. J. Theor. Phys. 40 40 (2001), 1683–1691 Zbl0989.81003MR1858217DOI10.1023/A:1011911512416
  13. Riečanová Z., 10.1023/A:1020136531601, Internat. J. Theor. Phys. 41 (2002), 1511–1524 MR1932844DOI10.1023/A:1020136531601
  14. Riečanová Z., 10.1016/S0165-0114(02)00141-0, Fuzzy Sets and Systems 136 (2003), 41–54 MR1978468DOI10.1016/S0165-0114(02)00141-0
  15. Riečanová Z., Distributive atomic effect algebras, Demonstratio Math. 36 (2003), 247–259 MR1984337
  16. Riečanová Z., 10.1023/A:1025775827938, Internat. J. Theor. Phys. 42 (2003), 1425–1433 MR2021221DOI10.1023/A:1025775827938
  17. Riečanová Z., Modular atomic effect algebras and the existence of subadditive states, Kybernetika 40 (2004), 459–468 MR2102364
  18. Schmidt J., 10.1007/BF01900297, Arch. Math. 17 (1956), 241–249 (1956) MR0084484DOI10.1007/BF01900297

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