Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Atomic varieties of sets with relative inverses

  • 22 Accesses

Abstract

The generalization of the construction of the lattice of varieties for partial algebras is used for sets with relative inverses. There are many quantum structures representable by sets with relative inverses (orthomodular lattices, orthoalgebras, D-posets, test spaces,...). Varieties covering the trivial variety are investigated for the case of closed (strongest type) subalgebras and closed homomorphisms. Some similar results for weaker types are given. The context with set representation problems is considered for the set-theoretic difference operations.

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

References

  1. Burmeister, P. (1986).A Model Theoretic Oriented Approach to Partial Algebras, Akademie Verlag, Berlin.

  2. Gudder, S. P. (1979).Stochastic Methods in Quantum Mechanics, Elsevier/North-Holland, Amsterdam.

  3. Gudder, S. P. (1988).Quantum Probability, Academic Press, New York.

  4. Kalmbach, G., and Riečanová, Z. (1994). An axiomatization for Abelian relative inverses,Demonstratio Mathematicae,27, 769–780.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Konôpka, P. Atomic varieties of sets with relative inverses. Int J Theor Phys 34, 1519–1524 (1995). https://doi.org/10.1007/BF00676262

Download citation

Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Relative Inverse
  • Difference Operation