Order

, Volume 26, Issue 2, pp 109–117

Two Notes on the Variety Generated by Planar Modular Lattices

Article

DOI: 10.1007/s11083-009-9110-3

Cite this article as:
Czédli, G. & Maróti, M. Order (2009) 26: 109. doi:10.1007/s11083-009-9110-3
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Abstract

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.

Keywords

Modular lattice Planar Lattice variety Subvariety 

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzeged, Aradi vértanúk tere 1Hungary

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