Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

On subdirectly irreducible OMAs

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

In this paper some properties of epi-representations and Schmidt-congruence relations of orthomodular partial algebras are investigated and an infinite list of OMA-epi-subdirectly irreducible orthomodular partial algebras will be constructed.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

  1. Berge, C., Graphs and Hypergraphs, North Holland Publ. Company, 1976.

  2. Beran, L., Orthomodular Lattices — Algebraic Approach, D.Reidel Publ. Company, 1985.

  3. Burmeister, P., ‘Partial algebras — survey of a unifying approach towards a two-valued model theory for partial algebras’, Algebra univers. 15 (1982), 306–358.

    Google Scholar 

  4. Burmeister, P., ‘A Model Theoretic Oriented Approach to Partial Algebras. Introduction to Theory and Application of Partial Algebras — Part I.’, Mathematical Research Vol. 32, Akademie-Verlag, Berlin, 1986.

    Google Scholar 

  5. Burmeister, P., ‘Partial Algebras — An Introductory Survey’, in G. Sabidussi, I. Rosenberg, (eds.), Algebras and Orders: Proceedings of the NATO Advanced Study Institute and Séminaire des Mathématiques, Montreal, Canada, Kluwer Publ. Co., 1993.

  6. Burmeister, P., Subdirect representations by epimorphisms in quasivarieties of partial algebras, Preprint No. 2010 of the Department of Mathematics of the Darmstadt University of Technology, 1998.

  7. Burmeister, P., and M. Maczyński, ‘Orthomodular (partial) algebras and their representations’, Demonstratio Math. XXVII (1994), 701–722.

    Google Scholar 

  8. Burmeister, P., and M. Maczyński, Quasi-rings and congruences in the theory of orthomodular algebras, Preprint No. 2014 of the Department of Mathematics of the Darmstadt University of Technology, 1998.

  9. Dichtl, M., ‘Astroids and Pastings’, Algebra univers. 18 (1984), 380–385.

    Google Scholar 

  10. Godowski, R., ‘Commutativity in orthomodular posets’, Reports on Mathematical Physics 18 (1980), 347–351.

    Google Scholar 

  11. Holzer, R. Greechie diagrams of orthomodular partial algebras, TU-Darmstadt, FB Mathematik, Preprint 2165, 2001

  12. Kalmbach, G., Orthomodular Lattices, Academic Press, 1983.

  13. Maczyński, M., and T. Traczyk, ‘A characterization of orthomodular partially ordered sets admitting a full set of states’, Bull. Polon. Acad. Ser. Sci. Math. Astr. Phys. 21 (1973), 3–9.

    Google Scholar 

  14. Pulmannová, S., ‘A remark on orthomodular partial algebras’, Demonstratio Math. XXVII (1994), 687–699.

    Google Scholar 

  15. Schmidt, J., ‘A homomorphism theorem for partial algebras’, Coll. Math. 21 (1970), 5–21.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Special issue of Studia Logica: “Algebraic Theory of Quasivarieties” Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko

Rights and permissions

Reprints and permissions

About this article

Cite this article

Holzer, R. On subdirectly irreducible OMAs. Stud Logica 78, 261–277 (2004). https://doi.org/10.1007/s11225-005-1277-z

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-005-1277-z

Keywords