Homomorphisms of distributive lattices as restrictions of congruences. III. Rectangular lattices and two convex sublattices

Abstract

Let $L$ be a finite lattice and let $I$ be an ideal of $L$. Then the restriction map is a bounded lattice homomorphism of the congruence lattice of~$L$ into the congruence lattice of $I$. In a 2009 paper, the authors proved the converse. In a 2012 paper, G. Czédli proved an analogous result for rectangular lattices. In this paper, we prove a stronger form of Czédli's result and provide a short, elementary, and direct proof.

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