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Abstrakty
The notion of a meander of an ideal in lattices is generalized in two directions: to ideals in orthoposets and to ideals in QMV-algebras, and used to a characterization of subclasses of the above structures, namely Boolean orthoposets and QMV-algebras m which every ideal is closed under perspectivity, and to a characterization of Riesz ideals in orthoposets and perspectivity closed ideals in QMV algebras.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
1--11
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Mathematical Institute Slovak Academy of Sciences SK-814 73 Bratislava, Slovakia
autor
- Mathematical Institute Slovak Academy of Sciences SK-814 73 Bratislava, Slovakia
autor
- Department of Mathematics University of Naples 1-801 26 Naples, Italy
Bibliografia
- 1. L. Beran , Orthomodular Lattices, Algebraic Approach, Reidel, Dordrecht, 1984.
- 2. L. Beran , Meanders in lattices, Collect. Math., Universität de Barcelona 46 (1995), 11-33.
- 3. L. Beran , Length of ideals in lattices, Collect. Math., Universität de Barcelona 46 (1995), 21-33.
- 4. M. Bennett , K. D. Foulis , A generalized Sasaki projection for effect algebras, Tatra Mt. Math. Publ. 15 (1998), 9-11.
- 5. L. Beran , S. Salvati , Boolean algebras revisited, Bolletino U.M.I. (7) 11-B (1997), 895-901.
- 6. G. Chevalier , Congruence relations in orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 197-226.
- 7. G. Chevalier , S. Pulmannova , Some ideal lattices in partial abelian monoids and effect algebras, Order 17 (2000), 75-92.
- 8. D. Foulis , M. Bennett , K. Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1325-1346.
- 9. R. Greechie , J. D. Foulis , J. S. Pulmannova , The center of an effect algebra, Order 12 (1995), 91-106.
- 10. R. Giuntini , Quantum MV algebras, Studia Logica 56 (1996), 393-417.
- 11. R. Giuntini , H. Greuling , Toward a formal language of unsharp properties, Found. Phys. 10 (1989), 931-945.
- 12. R. Giuntini , S. Pulmannova , Ideals and congruences in effect algebras and QMV algebras, Comm. Algebra 28 (2000), 1567-1592.
- 13. S. Gudder , S. Pulmannova , Quotients of partial abelian monoids, Algebra Universalis 38 (1997), 395-421.
- 14. F. Kopka , F. Chovanec , D-posets, Math. Slovaca 44 (1994), 21-34.
- 15. P. Ptak , S. Pulmannova , Orthomodular Structures as Quantum Logics, Kluwer Academic Publishers, Dordrecht, 1991.
- 16. S. Pulmannova , Congruences in partial abelian semigroups, Algebra Universalis 38 (1997), 119-140.
- 17. J. Tkadlec , Boolean orthoposets-concreteness and orthocompleteness, Math. Bohemica 119 (1994), 123-129.
- 18. J. Tkadlec , Conditions that force an orthomodular poset to be a Boolean algebra, Tatra Mt. Math. Publ. 10 (1997), 55-62.
- 19. A. Wilce, Perspectivity and congruence in partial abelian semigroups, Math. Slovaca 48 (1998), 117-136.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA1-0037-0008