Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
lattice effect algebra; MV-algebra; sharp element; sharp domination; atom; Euclidean algorithm
lattice effect algebra; MV-algebra; sharp element; sharp domination; atom; Euclidean algorithm
Summary:
Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is uniformly Archimedean then it is sharply dominating.
References:
[1] Cignoli, R., Mundici, D.: An elementary presentation of the equivalence between MV-algebras and $\ell $-groups with strong unit. Studia Logica 61 (1998), 49–64. DOI 10.1023/A:1005078213630 | MR 1639697 | Zbl 0964.06009
[2] Foulis, D. J., Bennett, M. K.: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1325–1346. MR 1304942
[3] Gudder, S. P.: Sharply dominating effect algebras. Tatra Mt. Math. Publ. 15 (1998), 23–30. MR 1655076 | Zbl 0939.03073
[4] Gudder, S. P.: S-dominating effect algebras. Internat. J. Theor. Phys. 37 (1998), 915–923. DOI 10.1023/A:1026637001130 | MR 1624277 | Zbl 0932.03072
[5] Kalina, M., Olejček, M., Paseka, J., Riečanová, Z.: Sharply Dominating MV-Effect Algebras. Internat. J. Theor. Phys. (2010), doi: 10.1007/s10773-010-0338-x
[6] Kôpka, F.: Boolean D-posets as factor spaces. Internat. J. Theor. Phys. 37 (1998), 93–101. DOI 10.1023/A:1026665306697 | MR 1637152
[7] Kôpka, F.: D-posets of fuzzy sets. Tatra Mt. Math. Publ. 1 (1992), 83–87. MR 1230466
[8] Kôpka, F., Chovanec, F.: D-posets. Math. Slovaca 44 (1994), 21–34. MR 1290269
[9] Riečanová, Z.: Archimedean and block-finite lattice effect algebras. Demonstr. Math. 33 (2000), 443–452. MR 1791464
[10] Riečanová, Z.: Subdirect Decompositions of Lattice Effect Algebras. Interernat. J. Theor. Phys. 42 (2003), 1415–1423. MR 2021221 | Zbl 1034.81003
Search
Partner of
