Congruences of the fork extensions. I. The Congruence Extension Property

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