Congruences in slim, planar, semimodular lattices: The Swing Lemma

2014/12/30 by George Grätzer, Grätzer, George
Mathematics · #06B10 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06B10

paper · pdf · doi:10.48550/arxiv.1412.8558

arxiv created 2015/04/24 · arxiv updated 2015/04/27

Abstract

In an earlier paper, to describe how a congruence spreads from a prime interval to another in a finite lattice, I introduced the concept of prime-perspectivity and its transitive extension, prime-projectivity and proved the Prime-projectivity Lemma. In this paper, I specialize the Prime-projectivity Lemma to slim, planar, semimodular lattices to obtain the Swing Lemma, a very powerful description of the congruence generated by a prime interval in this special class of lattices.

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