Resumen de Which freely generated lattices contain F (3)?

George Grätzer, David Kelly

• 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.