The Dilworth Theorems

Inhaltsverzeichnis

• Chain Partitions in Ordered Sets.
• A Decomposition Theorem for Partially Ordered Sets.
• Some Combinatorial Problems on Partially Ordered Sets.
• The Impact of the Chain Decomposition Theorem on Classical Combinatorics.
• Dilworth’s Decomposition Theorem in the Infinite Case.
• Effective Versions of the Chain Decomposition Theorem.
• Complementation.
• Lattices with Unique Complements.
• On Complemented Lattices.
• Uniquely Complemented Lattices.
• On Orthomodular Lattices.
• Decomposition Theory.
• Lattices with Unique Irreducible Decompositions.
• The Arithmetical Theory of Birkhoff Lattices.
• Ideals in Birkhoff Lattices.
• Decomposition Theory for Lattices without Chain Conditions.
• Note on the Kurosch-Ore Theorem.
• Structure and Decomposition Theory of Lattices.
• Dilworth’s Work on Decompositions in Semimodular Lattices.
• The Consequences of Dilworth’s Work on Lattices with Unique Irreducible Decompositions.
• Exchange Properties for Reduced Decompositions in Modular Lattices.
• The Impact of Dilworth’s Work on Semimodular Lattices on the Kurosch-Ore Theorem.
• Modular and Distributive Lattices.
• The Imbedding Problem for Modular Lattices.
• Proof of a Conjecture on Finite Modular Lattices.
• Distributivity in Lattices.
• Aspects of distributivity.
• The Role of Gluing Constructions in Modular Lattice Theory.
• Dilworth’s Covering Theorem for Modular Lattices.
• Geometric and Semimodular Lattices.
• Dependence Relations in a Semi-Modular Lattice.
• A Counterexample to the Generalization of Sperner’s Theorem.
• Dilworth’s Completion, Submodular Functions, and Combinatorial Optimization.
• Dilworth Truncations of Geometric Lattices.
• The Sperner Property in Geometric and Partition Lattices.
• Multiplicative Lattices.
• Abstract Residuation over Lattices.
• Residuated Lattices.
• Non-Commutative Residuated Lattices.
• Non-Commutative Arithmetic.
• Abstract Commutative Ideal Theory.
• Dilworth’s Early Papers on Residuated and Multiplicative Lattices.
• Abstract Ideal Theory: Principals and Particulars.
• Representation and Embedding Theorems for Noether Lattices and r-Lattices.
• Miscellaneous Papers.
• The Structure of Relatively Complemented Lattices.
• The Normal Completion of the Lattice of Continuous Functions.
• A Generalized Cantor Theorem.
• Generators of lattice varieties.
• Lattice Congruences and Dilworth’s Decomposition of Relatively Complemented Lattices.
• Cantor Theorems for Relations.
• Ideal and Filter Constructions in Lattice Varieties.
• Two Results from “Algebraic Theory of Lattices”.
• Dilworth’s Proof of the Embedding Theorem.
• On the Congruence Lattice of a Lattice.