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Algebra universalis

, 80:8 | Cite as

Modularity is not canonical

  • J. HardingEmail author
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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.

Keywords

Canonical extension Modular lattice 

Mathematics Subject Classification

06B23 06C05 03G10 

Notes

References

  1. 1.
    Gehrke, M., Harding, J.: Bounded lattice expansions. J. Algebra 238, 345–371 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Harding, J.: Canonical completions of lattices and ortholattices. Tatra Mt. Math. Publ. 15, 85–96 (1998)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Kaplansky, I.: On orthocomplemented complete modular lattice is a continuous geometry. Ann. Math. 61, 524–157541 (1955)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

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