SpringerLink
Log in

Homomorphisms and principal congruences of bounded lattices. II. Sketching the proof for sublattices

  • Published:
Algebra universalis Aims and scope Submit manuscript

Abstract

A recent result of G. Czédli relates the ordered set of principal congruences of a bounded lattice L with the ordered set of principal congruences of a bounded sublattice K of L. In this note, I sketch a new proof.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Czédli G.: Representing a monotone map by principal lattice congruences. Acta Mathematica Hungarica 147, 12–18 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  2. Czédli G.: The ordered set of principal congruences of a countable lattice. Algebra Universalis 75, 351–380 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  3. Czédli G.: An independence theorem for ordered sets of principal congruences and automorphism groups of bounded lattices. Acta Sci. Math (Szeged) 82, 3–18 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  4. Czédli G.: Representing some families of monotone maps by principal lattice congruences. Algebra Universalis 77, 51–77 (2017)

    Article  MATH  MathSciNet  Google Scholar 

  5. Czédli, G.: Cometic functors and representing order-preserving maps by principal lattice congruences. Algebra Universalis (2017, in press)

  6. Grätzer, G.: The Congruences of a Finite Lattice. A Proof-by-Picture Approach. Birkhäuser, Boston (2006)

  7. Grätzer, G.: Lattice Theory: Foundation. Birkhäuser Verlag, Basel (2011)

  8. Grätzer G.: The order of principal congruences of a bounded lattice. Algebra Universalis 70, 95–105 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  9. Grätzer, G.: The Congruences of a Finite Lattice, A Proof-by-Picture Approach, second edition. Birkhäuser (2016)

  10. Grätzer G.: Homomorphisms and principal congruences of bounded lattices. I. Isotone maps of principal congruences. Acta Sci. Math. (Szeged) 82, 353–360 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  11. Grätzer, G.: Homomorphisms and principal congruences of bounded lattices. III. The Independence Theorem. Algebra Universalis (in press)

  12. G. Grätzer and H. Lakser, Some preliminary results on the set of principal congruences of a finite lattice. Algebra Universalis (in press)

  13. G. Grätzer and H. Lakser, Minimal representations of a finite distributive lattice by principal congruences of a lattice (2017, manuscript)

  14. Grätzer, G., Wehrung, F. eds.: Lattice Theory: Special Topics and Applications. Volume 1. Birkhäuser Verlag, Basel (2014)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    G. Grätzer

Authors
  1. G. Grätzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Grätzer.

Additional information

Presented by F. Wehrung.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grätzer, G. Homomorphisms and principal congruences of bounded lattices. II. Sketching the proof for sublattices. Algebra Univers. 78, 291–295 (2017). https://doi.org/10.1007/s00012-017-0461-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00012-017-0461-0

2010 Mathematics Subject Classification

Key words and phrases

Search

Navigation