Finite transferable lattices are sharply transferable

C. R. Platt
1981 Proceedings of the American Mathematical Society  
A lattice £ is called transferable if and only if, whenever £ can be embedded into the lattice I(%) of all ideals of a lattice %, £ can be embedded into 9C itself. If for every lattice embedding/of £ into I(%) there exists an embedding g of £ into % satisfying the further condition that for x and y in L, fix) e g(y) holds if and only if x < y, then £ is called sharply transferable. It is shown that every finite transferable lattice is sharply transferable.
doi:10.1090/s0002-9939-1981-0597639-8 fatcat:wy2tlgmv25btxdz2smei4kvq6a