Congruences of the fork extensions. I. The Congruence Extension Property
George Gr\"atzer

TL;DR
This paper proves that fork extensions of slim, planar, semimodular lattices possess the Congruence Extension Property, advancing understanding of lattice congruences in this class.
Contribution
It establishes the Congruence Extension Property for fork extensions in slim, planar, semimodular lattices, a key step in lattice theory.
Findings
Fork extensions have the Congruence Extension Property
The result applies to slim, planar, semimodular lattices
Supports further analysis of lattice congruences
Abstract
For a slim, planar, semimodular lattice, G. Cz\'edli and E.\,T. Schmidt introduced the fork extension in 2012. In this note we prove that the fork extension has the Congruence Extension Property. This paper has been merged with Part II, under the title Congruences of fork extensions of slim semimodular lattices, see arXiv: 1307.8404
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Rough Sets and Fuzzy Logic
