ACTA issues

Notes on planar semimodular lattices. III. Rectangular lattices

G. Grätzer, E. Knapp

Acta Sci. Math. (Szeged) 75:1-2(2009), 29-48

Abstract. We introduce {\it rectangular lattices}, a special type of planar semimodular lattices. We show that every finite distributive lattice can be represented as the congruence lattice of a ``small'' rectangular lattice, improving a 1998 result of G. Grätzer, H. Lakser, and E.$ $T. Schmidt.

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

Keyword(s): semimodular lattice, planar, congruence, rectangular

Received October 15, 2007, and in revised form October 30, 2008. (Registered under 6058/2009.)