Skip to main content
Log in

Pseudo Difference Posets and Pseudo Boolean D-Posets

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Avallone, A. and Vitolo, P. (2003). Congruences and ideals of effect algebras. Order 20, 67–77.

    MATH  MathSciNet  Google Scholar 

  • Chang, C. C. (1958). Algebraic analysis of many valued logics. Transactions of the American Mathematical Society 88, 467–490.

    MATH  MathSciNet  Google Scholar 

  • Chovanec, F. and Kôpka, F. (1997). Boolean D-posets. Tatra Mountains Mathematical Publications, 10, 183–197.

    MATH  MathSciNet  Google Scholar 

  • Dvureoenskij, A. and Pulmannová, S. (1994). Difference posets, effects, and quantum measurements. International Journal of Theoretical Physics 33, 819–850.

    ADS  MathSciNet  Google Scholar 

  • Dvureoenskij, A. and Pulmannová, S. (2000). New Trends in Quantum Structures Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  • 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.

    Google Scholar 

  • Dvureoenskij, A. and Vetterlein, T. (2001b). Pseudo-effect algebras II. Group representations. International Journal of Theoretical Physics 40, 703–726.

    Google Scholar 

  • Dvureoenskij, A. (2002). Pseudo MV-algebra are intervals in l-groups. Journal of Australian Mathematical Society 72, 427–445.

    Article  Google Scholar 

  • Foulis, D. J. and Bennett, M. K. (1994). Effect algebra and unsharp quantum logics. International Journal of Theoretical Physics 24, 1325–1346.

    Google Scholar 

  • Foulis, D. J., Greechie, R. J., and Ruttimann, G. T. (1992). Filters and supports in orthoalgebras. International Journal of Theoretical Physics 31, 789–807.

    MATH  ADS  MathSciNet  Google Scholar 

  • Fuchs, L. (1963). Partially Ordered Algebraic Systems, Pergamon, Oxford.

    MATH  Google Scholar 

  • Georgescu, G. and lorgulescu, A. (2001). Pseudo-MV algebras. Multi Valued Logic 6, 95–135.

    MATH  Google Scholar 

  • Kalmbach, G. (1983). Orthomodular Lattices, Academic, London.

    MATH  Google Scholar 

  • Kôpka, F. and Chovanec, F. (1994). D-posets. Mathematical Slovaca 44, 21–34.

    MATH  Google Scholar 

  • Pulmannová, S. (2003). Generalized Sasaki projections and Riesz ideals on pseudoeffect algebras. International Journal of Theoretical Physics, 42, 1413–1423.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shang Yun.

Rights and permissions

Reprints 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

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-004-7710-7

Navigation