Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras

Journal of the Australian Mathematical Society

Volumn 74, Issue 1, 2003, Pages 121-143

  Dvurečenskij, Anatolij ^a  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Cantor Bernstein theorem; Central element; Effect algebra; General comparability; Monotone completeness; Pseudo MV algebra; Pseudo effect algebra

Indexed keywords

EID: 0037303339     PISSN: 14467887     EISSN: None     Source Type: Journal    
DOI: 10.1017/s1446788700003177     Document Type: Article

References (21)

1. R. Baudot, 'Non-commutative logic programming language NoClog', in: Symposium LICS (Santa Barbara, 2000, Short Presentation) pp. 3-9.
2. L. P. Belluce, 'α-complete MV-algebras', in: Non-classical logics and their applications to fuzzy subseis (ed. U. Hoehle et al.) (Kluwer, Dordrecht, 1995) pp. 7-21.
3. C. C. Chang, 'Algebraic analysis of many valued logics', Trans. Amer. Math. Soc. 88 (1958), 467-490.
4. A. De Simone, D. Mundici and M. Navara, 'A Cantor-Bernstein theorem for CT-complete MV-algebras', Czechoslovak Math. J. (to appear).
5. A. De Simone, M. Navara and P. Pták, 'On interval homogeneous orthomodular lattices', Comm. Math. Univ. Carolinae 42 (2001), 23-30.
6. A. Di Nola, G. Georgescu and A. Iorgulescu, 'Pseudo-BL-algebras, I, II', Mult.-Valued Logic (to appear).
7. A. Dvurečenskij, 'Pseudo MV-algebras are intervals in l-groups', J. Austral. Math. Soc. 72 (2002), 427-445.
8. A. Dvurečenskij and S. Pulmannová, New trends in quantum structures (Kluwer, Dordrecht, 2000).
9. A. Dvurečenskij and T. Vetterlein, 'Pseudoeffect algebras. I. Basic properties', Internat. J. Theor. Phys. 40 (2001), 685-701.
10. _, 'Pseudoeffect algebras. II. Group representations', Internat. J. Theor. Phys. 40 (2001), 703-726.
11. D. J. Foulis and M. K. Bennett, 'Effect algebras and unsharp quantum logics', Found. Phys. 24 (1994), 1325-1346.
12. G. Georgescu and A. Iorgulescu, 'Pseudo-MV algebras: A non-commutative extension of MV-algebras', in: Proc. Fourth Inter. Symp. on Econ. Inform., May 6-9, 1999, Bucharest (ed. I. Smeureanu et al.) (INFOREC Printing House, Bucharest, 1999) pp. 961-968.
13. _, 'Pseudo-MV algebras', Mult.-Valued Logic 6 (2001), 95-135.
14. K. R. Goodearl, Partially ordered abelian groups with interpolation, Math. Surveys and Monographs 20 (Amer. Math. Soc., Providence, RI, 1986).
15. R. J. Greechie, D. J. Foulis and S. Pulmannová, 'The center of an effect algebra', Order 12 (1995), 91-106.
16. J. Jakubík, 'Cantor-Bernstein theorem for MV-algebras', Czechoslovak Math. J. 49 (1999), 517-529.
17. _, 'A theorem of Cantor-Bernstein theorem type for orthogonally σ-complete pseudo MV-algebras', Tatra Mt. Math. Publ. (to appear).
18. G. Jenča, 'A Cantor-Bernstein type theorem for effect algebras', Algebra Universalis (to appear).
19. F. Kôpka and F. Chovanec, 'D-posets', Math. Slovaca 44 (1994), 21-34.
20. D. Mundici, 'Interpretation of AF C*-algebras in Łukasiewicz sentential calculus', J. Funct. Anal. 65 (1986), 15-63.
21. J. Rachůnek, 'A non-commutative generalization of MV-algebras', Czechoslovak Math. J. 52 (2002), 255-273.