Two Notes on the Variety Generated by Planar Modular Lattices
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- Czédli, G. & Maróti, M. Order (2009) 26: 109. doi:10.1007/s11083-009-9110-3
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Let Var(Mplan) denote the variety generated by the class Mplan of planar modular lattices. In 1977, based on his structural investigations, R. Freese proved that Var(Mplan) 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(Mplan) is generated by its planar (subdirectly irreducible) members.