The Dilworth Theorems

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.- The Normal Completion of the Lattice of Continuous Functions.- 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.