Congruences and Trajectories in Planar Semimodular Lattices
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 1
Abstract
A 1955 result of J. Jakub´ık states that for the prime intervals p and q of a finite lattice, con(p) ≥ con(q) iff p is congruence-projective to q (via intervals of arbitrary size). The problem is how to determine whether con(p) ≥ con(q) involving only prime intervals. Two recent papers approached this problem in different ways. G. Cz´edli’s used trajectories for slim rectangular lattices—a special subclass of slim, planar, semimodular lattices. I used the concept of prime-projectivity for arbitrary finite lattices. In this note I show how my approach can be used to reprove Cz´edli’s result and generalize it to arbitrary slim, planar, semimodular lattices.
Authors and Affiliations
G. Grätzer
Keywords
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