For a class script C sign of finite lattices, the question arises whether any lattice in script C sign can be embedded into some atomistic, biatomic lattice in script C sign. We provide answers to the question above for script C sign 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.
- Congruence extension property
- Convex geometry
- Lower bounded
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology
- Computational Theory and Mathematics