Compatibility and central elements in pseudo-effect algebras

Paolo Vitolo

Kybernetika (2010)

  • Volume: 46, Issue: 6, page 996-1008
  • ISSN: 0023-5954

Abstract

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An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.

How to cite

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Vitolo, Paolo. "Compatibility and central elements in pseudo-effect algebras." Kybernetika 46.6 (2010): 996-1008. <http://eudml.org/doc/196427>.

@article{Vitolo2010,
abstract = {An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.},
author = {Vitolo, Paolo},
journal = {Kybernetika},
keywords = {pseudo-effect algebra; lattice pseudo-effect algebra; pseudo-MV-algebra; compatible elements; central element; pseudo-effect algebra; lattice pseudo-effect algebra; pseudo MV-algebra; compatibility; central element},
language = {eng},
number = {6},
pages = {996-1008},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Compatibility and central elements in pseudo-effect algebras},
url = {http://eudml.org/doc/196427},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Vitolo, Paolo
TI - Compatibility and central elements in pseudo-effect algebras
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 6
SP - 996
EP - 1008
AB - An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.
LA - eng
KW - pseudo-effect algebra; lattice pseudo-effect algebra; pseudo-MV-algebra; compatible elements; central element; pseudo-effect algebra; lattice pseudo-effect algebra; pseudo MV-algebra; compatibility; central element
UR - http://eudml.org/doc/196427
ER -

References

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  1. Avallone, A., Barbieri, G., Vitolo., P., Central elements in pseudo-D-lattices and Hahn decomposition theorem, Boll. Unione Mat. Ital. 9 (2010), III(3), 447-470. (2010) MR2742776
  2. Avallone, A., Vitolo, P., Pseudo-D-lattices and topologies generated by measures, Italian J. Pure Appl. Math., to appear. 
  3. Bennet, M. K., Foulis, D. J., 10.1007/BF02283036, Found. Phys. 24 (1994), 10, 1331–1352. (1994) MR1304942DOI10.1007/BF02283036
  4. Butnariu, D., Klement, P., Triangular Norm-based Measures and Games with Fuzzy Coalitions, Kluwer Academic Publishers, Dordrecht 1993. (1993) Zbl0804.90145
  5. Dvurečenskij, A., Blocks of pseudo-effect algebras with the Riesz interpolation property, Soft Computing 7 (2003), 441–445. (2003) Zbl1030.06008
  6. Dvurečenskij, A., 10.1017/S1446788700003177, J. Austral. Math. Soc. 74 (2003), 121–143. (2003) MR1948263DOI10.1017/S1446788700003177
  7. Dvurečenskij, A., New quantum structures, In: Handbook of quantum logic and quantum structures (K. Engesser, D. M. Gabbay, and D. Lehmann, eds.), Elsevier, 2007. (2007) Zbl1134.81006MR2408886
  8. Dvurečenskij, A., Pulmannová, S., New Trends in Quantum Structures, Kluwer Academic Publishers, Dordrecht 2000. (2000) MR1861369
  9. Dvurečenskij, A., Vetterlein, T., 10.1023/A:1015561420306, Found. Phys. Lett. 14 (2001), 5, 425–446. (2001) MR1857794DOI10.1023/A:1015561420306
  10. Dvurečenskij, A., Vetterlein, T., Pseudoeffect algebras, I. Basic properties. Internat. J. Theoret. Phys. 40 (2001),3, 685–701. (2001) Zbl0994.81009MR1831592
  11. Dvurečenskij, A., Vetterlein, T., 10.1023/A:1004144832348, II. Group representations. Internat. J. Theoret. Phys. 40 (2001), 3, 703–726. (2001) Zbl0994.81009MR1831593DOI10.1023/A:1004144832348
  12. Dvurečenskij, A., Vetterlein, T., On pseudo-effect algebras which can be covered by pseudo MV-algebras, Demonstratio Math. 36 (2003), 2, 261–282. (2003) Zbl1039.03049MR1984338
  13. Epstein, L. G., Zhang, J., 10.1111/1468-0262.00193, Econometrica 69 (2001), 2, 265–306. (2001) Zbl1020.91048MR1819756DOI10.1111/1468-0262.00193
  14. Georgescu, G., Iorgulescu, A., Pseudo-MV algebras, Mult.-Valued Log. 6 G. C. Moisil memorial issue. (2001), 1-2, 95–135. (2001) Zbl1014.06008MR1817439
  15. Kôpka, F., Chovanec, F., D-posets, Mathematica Slovaca 44 (1994), 21–34. (1994) MR1290269
  16. Pulmannová, S., 10.1023/A:1025723811099, Internat. J. Theoret. Phys. 42 (2003), 7, 1413–1423. (2003) Zbl1053.81008MR2021220DOI10.1023/A:1025723811099
  17. Riečanová, Z., Compatibility and central elements in effect algebras, Tatra Mt. Math. Publ. 16 (1999), 151–158. (1999) MR1725293
  18. Yun, S., Yongming, L., Maoyin, C., 10.1007/s10773-004-7710-7, Internat. J. Theoret. Phys. 43 (2004), 12, 2447–2460. (2004) Zbl1059.81018MR2110077DOI10.1007/s10773-004-7710-7

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