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Finite transferable lattices are sharply transferable

1981
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Proceedings of the American Mathematical Society
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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