ACTA issues

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

G. Gr├Ątzer

Acta Sci. Math. (Szeged) 81:3-4(2015), 381-397

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.

DOI: 10.14232/actasm-015-757-1

AMS Subject Classification (1991): 06C10, 06B10

Keyword(s): prime-perspective, congruence, congruence-perspective, perspective, prime interval

Received February 4, 2015, and in revised form April 21, 2015. (Registered under 7/2015.)