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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Czédli G.: Representing a monotone map by principal lattice congruences. Acta Mathematica Hungarica 147, 12–18 (2015)
Czédli G.: The ordered set of principal congruences of a countable lattice. Algebra Universalis 75, 351–380 (2016)
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)
Czédli G.: Representing some families of monotone maps by principal lattice congruences. Algebra Universalis 77, 51–77 (2017)
Czédli, G.: Cometic functors and representing order-preserving maps by principal lattice congruences. Algebra Universalis (2017, in press)
Grätzer, G.: The Congruences of a Finite Lattice. A Proof-by-Picture Approach. Birkhäuser, Boston (2006)
Grätzer, G.: Lattice Theory: Foundation. Birkhäuser Verlag, Basel (2011)
Grätzer G.: The order of principal congruences of a bounded lattice. Algebra Universalis 70, 95–105 (2013)
Grätzer, G.: The Congruences of a Finite Lattice, A Proof-by-Picture Approach, second edition. Birkhäuser (2016)
Grätzer G.: Homomorphisms and principal congruences of bounded lattices. I. Isotone maps of principal congruences. Acta Sci. Math. (Szeged) 82, 353–360 (2016)
Grätzer, G.: Homomorphisms and principal congruences of bounded lattices. III. The Independence Theorem. Algebra Universalis (in press)
G. Grätzer and H. Lakser, Some preliminary results on the set of principal congruences of a finite lattice. Algebra Universalis (in press)
G. Grätzer and H. Lakser, Minimal representations of a finite distributive lattice by principal congruences of a lattice (2017, manuscript)
Grätzer, G., Wehrung, F. eds.: Lattice Theory: Special Topics and Applications. Volume 1. Birkhäuser Verlag, Basel (2014)
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by F. Wehrung.
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00012-017-0461-0