Skip to main content
Log in

Modularity is not canonical

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

Abstract

In 1998 the author showed that the canonical extension of a bounded modular lattice need not be modular. The proof was indirect, using a deep result of Kaplansky. In this note we give an explicit example.

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.

Institutional subscriptions

References

  1. Gehrke, M., Harding, J.: Bounded lattice expansions. J. Algebra 238, 345–371 (2001)

    Article  MathSciNet  Google Scholar 

  2. Harding, J.: Canonical completions of lattices and ortholattices. Tatra Mt. Math. Publ. 15, 85–96 (1998)

    MathSciNet  MATH  Google Scholar 

  3. Kaplansky, I.: On orthocomplemented complete modular lattice is a continuous geometry. Ann. Math. 61, 524–157541 (1955)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Harding.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Harding, J. Modularity is not canonical. Algebra Univers. 80, 8 (2019). https://doi.org/10.1007/s00012-019-0582-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00012-019-0582-8

Keywords

Mathematics Subject Classification

Navigation