The varieties dicomplemented lattices generated by chains.
by
Leonard Kwuida
Institut fuer Algebra, TU Dresden
Coauthors: Bernhard Ganter (Institut fuer Algebra, TU Dresen)

The variety of all lattices has a unique minimal subvariety, the variety of all distributive lattices, generated by a two element chain. The two element Boolean algebra generates the variety of all Boolean algebras, and this is the unique minimal subvariety of the variety of all dicomplemented lattices. There are, however, distributive dicomplemented lattices that are not Boolean. We want to know if the variety of distributive dicomplemented lattices is finitely generated. How does a minimal variety covering the variety generated by a two element dicomplemented lattice look like? We investigate the varieties of dicomplemented lattices generated by chains. We show that they are exactly four of them, all being proper subvarieties of the variety of dicomplemented lattices. We compute the cardinality of the free dicomplemented lattice in the variety generated by a 3 element chain.

Date received: January 22, 2002