Which freely generated lattices contain F (3)?

• Autores: George Grätzer, David Kelly
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 59, Nº. 1-2, 2008, págs. 117-132
• Idioma: inglés
• DOI: 10.1007/s00012-008-2079-8
• Texto completo no disponible (Saber más ...)
• Resumen

  • In 1979, I. Rival and R. Wille characterized which orders freely generate a lattice that contains F(3), the free lattice on three generators. Their characterization is that the order contains 1+1+1, 2+3, or 1+5 (where n is the n-element chain). We give a new proof of their result. In fact, we generalize their result to m-lattices (where joins and meets of nonempty sets of cardinality less than m are allowed).

    In our proof, we apply a new result; namely, that our lattice-attachment construction preserves breadth when the skeleton is a chain.