Abstract:
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, atomistic,
biatomic, join-semidistributive lattices but not in all finite join-semidistributive
lattices