International Journal of Theoretical Physics

, Volume 47, Issue 1, pp 280–290 | Cite as

Tensor Product of Distributive Sequential Effect Algebras and Product Effect Algebras

  • Eissa D. Habil


A distributive sequential effect algebra (DSEA) is an effect algebra on which a distributive sequential product with natural properties is defined. We define the tensor product of two arbitrary DSEA’s and we give a necessary and sufficient condition for it to exist. As a corollary we obtain the result (see Gudder, S. in Math. Slovaca 54:1–11, 2004, to appear) that the tensor product of a pair of commutative sequential effect algebras exists if and only if they admit a bimorphism. We further obtain a similar result for the tensor product of a pair of product effect algebras.


Effect algebras Sequential products Distributive sequential products Tensor products Product effect algebras Fuzzy sets 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gudder, S.: Tensor products of sequential effect algebras. Math. Slovaca 54, 1–11 (2004) MATHMathSciNetGoogle Scholar
  2. 2.
    Gudder, S., Greechie, R.: Sequential products on effect algebras. Rep. Math. Phys. 49, 87–111 (2002) MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Gudder, S., Greechie, R.: Uniqueness and order in sequential effect algebras. Int. J. Theor. Phys. 44, 755–770 (2005) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gudder, S.: A historic approach to quantum mechanics. J. Math. Phys. 39, 5772–5788 (1998) MATHCrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Busch, P., Lahti, P.J., Middlestaedt, P.: The Quantum Theory of Measurements. Springer, Berlin (1991) Google Scholar
  6. 6.
    Busch, P., Grabawski, M., Lahti, P.J.: Operational Quantum Physics. Springer, Berlin (1995) MATHGoogle Scholar
  7. 7.
    Gudder, S., Nagy, G.: Sequential independent effects. Proc. Am. Math. Soc. 130, 1125–1130 (2001) CrossRefMathSciNetGoogle Scholar
  8. 8.
    Gudder, S., Nagy, G.: Sequential quantum measurements. J. Math. Phys. 42, 5212–5222 (2001) MATHCrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Dvurečenskij, A.: Product effect algebras. Slovak Academy of Sciences Preprint Series, Preprint 2/2002 Google Scholar
  10. 10.
    Dvurečenskij, A.: Tensor product of difference posets. Trans. Am. Math. Soc. 347, 1043–1057 (1995) CrossRefGoogle Scholar
  11. 11.
    Foulis, D.J., Bennett, M.K.: Effect algebras and unsharp quantum logics. Found. Phys. 24, 1325–1346 (1994) CrossRefMathSciNetGoogle Scholar
  12. 12.
    Gudder, S.: Morphisms, tensor products and σ-effect algebras. Rep. Math. Phys. 42, 321–346 (1998) MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Habil, E.: Morphisms and pasting of orthoalgebras. Math. Slovaca 47, 405–416 (1997) MATHMathSciNetGoogle Scholar
  14. 14.
    Gudder, S.: Open problems for sequential effect algebras. Int. J. Theor. Phys. 44, 2199–2206 (2005) MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsIslamic University of GazaGazaPalestine

Personalised recommendations