2 2 Ja n 20 05 EMBEDDING FINITE LATTICES INTO FINITE BIATOMIC LATTICES

For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, — The class of all finite lattices; — The class of all finite lower bounded lattices (solved by the first author's earlier work). — The class of all finite join-semidistributive lattices (this problem was, until now, open). We solve the latter problem by finding a quasi-identity valid in all finite, atom-istic, biatomic, join-semidistributive lattices but not in all finite join-semidis-tributive lattices.