Two Notes on the Variety Generated by Planar Modular Lattices

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. Dedicated to the memory of András P. Huhn This research was partially supported by the NFSR of Hungary (OTKA), grant no. T 049433, T 48809 and K 60148.     

On normal crossings in a Banach space

We show that if A is a closed complex analytic subset of a Banach space X with an unconditional basis (e.g., X=?₂) that has only normal crossings for singularities, then the structure and ideal sheaves of A are cohesive sheaves over X, and consequently, they are acyclic over any pseudoconvex open subset of X.