Embedding Finite Lattices into Finite Biatomic Lattices
Copyright policy )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, atomistic, biatomic, join-semidistributive lattices but not in all finite join-semidistributive lattices.
- University of Caen Lower Normandy France
- Normandie Université France
- French National Centre for Scientific Research France
- City Colleges of Chicago United States
- Université de Caen Normandie France
finite lattices, convex geometry, Primary 06B99, congruence extension property., Structure theory of lattices, 51D20, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], lower bounded lattices, biatomic, General Mathematics (math.GM), congruence extension property, FOS: Mathematics, 05C20, join-semidistributive lattices, 51E99. Secondary: 51E30, 05B25, Mathematics - General Mathematics, biatomic lattice, Lattice, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Semimodular lattices, geometric lattices, atomistic, lower bounded, Combinatorial aspects of finite geometries, join-semidistributive, Primary 06B99, 05B25, 51E99. Secondary: 51E30, 51D20, 05C20
finite lattices, convex geometry, Primary 06B99, congruence extension property., Structure theory of lattices, 51D20, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], lower bounded lattices, biatomic, General Mathematics (math.GM), congruence extension property, FOS: Mathematics, 05C20, join-semidistributive lattices, 51E99. Secondary: 51E30, 05B25, Mathematics - General Mathematics, biatomic lattice, Lattice, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Semimodular lattices, geometric lattices, atomistic, lower bounded, Combinatorial aspects of finite geometries, join-semidistributive, Primary 06B99, 05B25, 51E99. Secondary: 51E30, 51D20, 05C20
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