The Dilworth Theorems: Selected Papers of Robert P.Dilworth
R. P. Dilworth, Kenneth P. Bogart, Ralph S. Freese, Joseph P. S. Kung · 1990
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 Uniquely Complemented On Orthomodular Decomposition Theory.- Lattices with Unique Irreducible Decompositions.- The Arithmetical Theory of Birkhoff Ideals in Birkhoff Decomposition Theory for Lattices without Chain Conditions.- Note on the Kurosch-Ore Theorem.- Structure and Decomposition Theory of Dilworth's Work on Decompositions in Semimodular The Consequences of Dilworth's Work on Lattices with Unique Irreducible Decompositions.- Exchange Properties for Reduced Decompositions in Modular The Impact of Dilworth's Work on Semimodular Lattices on the Kurosch-Ore Theorem.- Modular and Distributive The Imbedding Problem for Modular Proof of a Conjecture on Finite Modular Distributivity in Aspects of distributivity.- The Role of Gluing Constructions in Modular Lattice Theory.- Dilworth's Covering Theorem for Modular Geometric and Semimodular 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 The Sperner Property in Geometric and Partition Multiplicative Abstract Residuation over Residuated Non-Commutative Residuated Non-Commutative Arithmetic.- Abstract Commutative Ideal Theory.- Dilworth's Early Papers on Residuated and Multiplicative Abstract Ideal Theory: Principals and Particulars.- Representation and Embedding Theorems for Noether Lattices and r-Lattices.- Miscellaneous Papers.- The Structure of Relatively Complemented 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 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.