2005/01/22 by Friedrich Wehrung, Kira Adaricheva
Mathematics · #math.GM #msc:06B99 #msc:05B25 #msc:51E99. #msc:51E30 #msc:51D20 #msc:05C20
published as Order 20, no. 1 (2003) 31--48
arxiv created 2005/01/22 · arxiv updated 2009/12/01
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.