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

2015; Birkhäuser; Volume: 81; Issue: 3-4 Linguagem: Inglês

10.14232/actasm-015-757-1

2064-8316

George Grätzer,

Fuzzy and Soft Set Theory

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.