Abstract
The definitions of pseudo difference posets, pseudo boolean D-posets, and D-ideals are introduced. It is proved that pseudo difference posets are algebraically equivalent to pseudo effect algebras and pseudo boolean D-posets are algebraically equivalent to pseudo MV-algebras. In pseudo difference lattices, a D-ideal is equal to a Riesz ideal. At the same time, some good properties are obtained.
Similar content being viewed by others
References
Avallone, A. and Vitolo, P. (2003). Congruences and ideals of effect algebras. Order 20, 67–77.
Chang, C. C. (1958). Algebraic analysis of many valued logics. Transactions of the American Mathematical Society 88, 467–490.
Chovanec, F. and Kôpka, F. (1997). Boolean D-posets. Tatra Mountains Mathematical Publications, 10, 183–197.
Dvureoenskij, A. and Pulmannová, S. (1994). Difference posets, effects, and quantum measurements. International Journal of Theoretical Physics 33, 819–850.
Dvureoenskij, A. and Pulmannová, S. (2000). New Trends in Quantum Structures Kluwer, Dordrecht, The Netherlands.
Dvureoenskij, A. and Vetterlein, T. (2000a). Generalized pseudo effect algebras.
Dvureoenskij, A. and Vetterlein, T. (2000b). Algebras in the positive cone of po-group.
Dvureoenskij, A. and Vetterlein, T. (2001a). Pseudo-effect algebras I. Basic properties. International Journal of Theoretical Physics 40, 685–701.
Dvureoenskij, A. and Vetterlein, T. (2001b). Pseudo-effect algebras II. Group representations. International Journal of Theoretical Physics 40, 703–726.
Dvureoenskij, A. (2002). Pseudo MV-algebra are intervals in l-groups. Journal of Australian Mathematical Society 72, 427–445.
Foulis, D. J. and Bennett, M. K. (1994). Effect algebra and unsharp quantum logics. International Journal of Theoretical Physics 24, 1325–1346.
Foulis, D. J., Greechie, R. J., and Ruttimann, G. T. (1992). Filters and supports in orthoalgebras. International Journal of Theoretical Physics 31, 789–807.
Fuchs, L. (1963). Partially Ordered Algebraic Systems, Pergamon, Oxford.
Georgescu, G. and lorgulescu, A. (2001). Pseudo-MV algebras. Multi Valued Logic 6, 95–135.
Kalmbach, G. (1983). Orthomodular Lattices, Academic, London.
Kôpka, F. and Chovanec, F. (1994). D-posets. Mathematical Slovaca 44, 21–34.
Pulmannová, S. (2003). Generalized Sasaki projections and Riesz ideals on pseudoeffect algebras. International Journal of Theoretical Physics, 42, 1413–1423.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yun, S., Yongming, L. & Maoyin, C. Pseudo Difference Posets and Pseudo Boolean D-Posets. Int J Theor Phys 43, 2447–2460 (2004). https://doi.org/10.1007/s10773-004-7710-7
Issue Date:
DOI: https://doi.org/10.1007/s10773-004-7710-7