Skip to main content
Log in

A homomorphic image of a semimodular lattice need not be semimodular: an answer to a problem of Birkhoff

  • Mailbox
  • Published:
algebra universalis Aims and scope Submit manuscript

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.

References

  1. G. Birkhoff,Lattice Theory, Amer. Math. Soc., 3rd Edition 1967.

  2. A. H. Clifford andG. B. Preston,Algebraic Theory of Semigroups, Math. Surveys 7, Amer. Math. Soc., Providence R. I., Vol. I 1961, Vol. II 1967.

    MATH  Google Scholar 

  3. J. M. Howie,An Introduction to Semigroup Theory, Academic Press, London, 1976.

    MATH  Google Scholar 

  4. P. R. Jones,Semimodular inverse semigroups, J. London Math. Soc. (2)17 (1978).

  5. S. R. Kogalovskii,On the theorem of Birkhoff (Russian), Uspehi Mat. Nauk,20 (1965), no. 4, 206–207.

    MATH  MathSciNet  Google Scholar 

  6. R. C. Lyndon,Properties preserved under homomorphism, Pacific J. Math.9 (1959), 143–154.

    MATH  MathSciNet  Google Scholar 

  7. F. Maeda andS. Maeda,Theory of Symmetric Lattices, Springer, Berlin, 1970.

    MATH  Google Scholar 

  8. W. D. Munn,Free inverse semigroups, Proc. London Math. Soc., (3)29 (1974), 385–404.

    MATH  MathSciNet  Google Scholar 

  9. P. Pudlak andJ. Tuma,Every finite lattice can be embedded in the lattice of all equivalences on a finite set, Comment Math. Univ. Carolinae18 (1977), 409–414.

    MATH  MathSciNet  Google Scholar 

  10. B. M. Schein,On the theory of generalized groups (Russian), Doklady Akad. Nauk SSSR153 (1963), no. 3, 296–299.

    MATH  Google Scholar 

  11. S. Sato,On groups and the lattice of subgroups, Osaka Math. Journal1 (1949), 135–149.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jones, P.R. A homomorphic image of a semimodular lattice need not be semimodular: an answer to a problem of Birkhoff. Algebra Universalis 9, 127–130 (1979). https://doi.org/10.1007/BF02488021

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02488021

Keywords

Navigation