Two Notes on the Variety Generated by Planar Modular Lattices

摘要

Let Var(M_(plan)) denote the variety generated by the class M_(plan) of planar modular lattices. In 1977, based on his structural investigations, R. Freese proved that Var(M_(plan)) has continuumly many subvarieties. The present paper provides a new approach to this result utilizing lattice identities. We also show that each subvariety of Var(M_(plan)) is generated by its planar (subdirectly irreducible) members.