Kybernetika 48 no. 2, 294-298, 2012

Fractal construction of an atomic Archimedean effect algebra with non-atomic subalgebra of sharp elements

Vladimír Olejček


Does there exist an atomic Archimedean lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question is given.


sharp element, atomic Archimedean lattice effect algebra


06D35, 06C15, 03G12, 81P10


  1. A. Dvurečenskij and S. Pulmannová: New trends in Quantum Structures Theory. Klu\-wer Academic Publications, Dordrecht / Ister Science, Bratislava 2000.   CrossRef
  2. D. J. Foulis and M. K. Bennett: Ef\/fect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1331-1352.   CrossRef
  3. G. Jenča and Z. Riečanová: On sharp elements in lattice ordered effect algebras. BUSEFAL 80 (1999), 24-29.   CrossRef
  4. F. K\^opka and F. Chovanec: D-posets. Math. Slovaca 44 (1994), 21-34.   CrossRef
  5. V. Olejček: An atomic MV-effect algebra with non-atomic center. Kybernetika 43 (2007), 3, 343-346.   CrossRef
  6. V. Olejček: Uniformly Archimedean MV-effect algebra is sharply dominating. Kybernetika 46 (2010), 6, 948-952.   CrossRef
  7. Z. Riečanová: Modular atomic effect algebras and the existence of subadditive states. Kybernetika 40 (2004), 4, 459-468.   CrossRef
  8. Z. Riečanová, I. Marinová and M. Zajac: Some aspects of generalized prelattice effect algebras. In: Lecture Notes in Artificial Intelligence (LNAI) 4342 ``Theory and Application of Relational Structures as Knowledge Instruments II"(H. de Swart et all, eds.), Springer 2006, pp. 290-317.   CrossRef