A lattice L is transferable
iff, whenever L can be embedded in the ideal lattice of a lattice M, then L can be
embedded in M. This concept was introduced by the first author in 1965 who also
proved in 1966 that in a transferable lattice there are no doubly reducible elements.
In fact, he proved that every lattice can be embedded in the ideal lattice of a lattice
containing no doubly reducible elements. In a recent paper of the first two authors,
the idea emerged that one should study transferability via classes K of lattices with
the property that every Iattice is embeddable in the ideal lattice of a lattice
in K. This approach was used to establish that transferable lattices are
semi-distributive. This investigation is carried further in this paper. Our main result
shows that every lattice can be embedded in the ideal lattice of a lattice
satisfying the two semi-distributive properties and two variants of Whitman’s
condition.
