Zilber's Theorem for planar lattices, revisited

math.RA

/ Authors

/ Abstract

Zilber's Theorem states that a finite lattice $L$ is planar if{}f it has a complementary order relation. We provide a new proof for this crucial result and discuss some applications, including a canonical form for finite planar lattices and an analysis of coverings in the left-right order.

Zilber's Theorem for planar lattices, revisited

math.RA

/ Authors

Kirby A. Baker, George Grätzer

/ Abstract

Zilber's Theorem states that a finite lattice $L$ is planar if{}f it has a complementary order relation. We provide a new proof for this crucial result and discuss some applications, including a canonical form for finite planar lattices and an analysis of coverings in the left-right order.