Two Embedding Theorems for Lattices
G. Gratzer, C. R. Platt · Proceedings of the American Mathematical Society · 1978
A lattice L satisfies (SDA) \ia/\b = a/\c implies that a /\b = a /\(b\J c) ((SDV) is defined dually).Theorem.Every lattice can be embedded in the ideal lattice of a lattice satisfying (SDA) (respectively, (SDV)).Call a lattice K transferable iff whenever K can be embedded in the ideal lattice of a lattice L, then K can be embedded in L. Corollary.Every transferable lattice satisfies (SDA) and (SDV).1. Introduction.Two properties (P) can be found in the literature for which the following embedding theorem holds:Every lattice can be embedded in the ideal lattice of a lattice with property (P)-