Geodesic
Every uniformly Archimedean atomic MV-effect algebra is sharply dominating
Kybernetika, Tome 46 (2010) no. 6, pp. 948-952

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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.
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.
Classification : 03G12, 06D35, 06F25, 81P10
Keywords: lattice effect algebra; MV-algebra; sharp element; sharp domination; atom; Euclidean algorithm 
Olejček, Vladimír. Every uniformly Archimedean atomic MV-effect algebra is sharply dominating. Kybernetika, Tome 46 (2010) no. 6, pp. 948-952. http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a2/
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     title = {Every uniformly {Archimedean} atomic {MV-effect} algebra is sharply dominating},
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     volume = {46},
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     zbl = {1228.03044},
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     url = {http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a2/}
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[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 | MR | Zbl

[2] Foulis, D. J., Bennett, M. K.: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1325–1346. | MR

[3] Gudder, S. P.: Sharply dominating effect algebras. Tatra Mt. Math. Publ. 15 (1998), 23–30. | MR | Zbl

[4] Gudder, S. P.: S-dominating effect algebras. Internat. J. Theor. Phys. 37 (1998), 915–923. | DOI | MR | Zbl

[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 | MR

[7] Kôpka, F.: D-posets of fuzzy sets. Tatra Mt. Math. Publ. 1 (1992), 83–87. | MR

[8] Kôpka, F., Chovanec, F.: D-posets. Math. Slovaca 44 (1994), 21–34. | MR

[9] Riečanová, Z.: Archimedean and block-finite lattice effect algebras. Demonstr. Math. 33 (2000), 443–452. | MR

[10] Riečanová, Z.: Subdirect Decompositions of Lattice Effect Algebras. Interernat. J. Theor. Phys. 42 (2003), 1415–1423. | MR | Zbl