Reprinted Papers 41 Lattices with Unique Complements On Complemented Lattices 73 Articles 79 M. Adams Uniquely Complemented Lattices G. Kalmbach On Orthomodular Lattices 85 3 Decomposition Theory Background 89 Reprinted Papers Lattices with Unique Irreducible Decompositions 93 The Arithmetical Theory of Birkhoff Lattices 101 Ideals in Birkhoff Lattices 115 Decomposition Theory for Lattices without Chain Conditions 145 (with P. Crawley) 167 Note on the Kurosch-Ore Theorem Structure and Decomposition Theory of Lattices 173 Articles B. Jonsson Dilworth's Work on Decompositions in Semi 187 modular Lattices B. Monjardet The Consequences of Dilworth's Work on 192 Lattices with Unique Irreducible Decompositions J. Kung Exchange Properties for Reduced Decompositions in 201 Modular Lattices M. Stern The Impact of Dilworth's Work on Semimodular 203 Lattices on the Kurosch-Ore Theorem 4 Modular and Distributive Lattices Background 205 Reprinted Papers The Imbedding Problem for Modular Lattices (with M. Hall) 211 Proof of a Conjecture on Finite Modular Lattices Distributivity in Lattices (with J. McLaughlin) Aspects of Distributivity Articles A. Day and R. Freese The Role of Gluing Constructions in 251 Modular Lattice Theory I. Rival Dilworth's Covering Theorem for Modular Lattices 261 vi THE DILWORTH THEOREMS 5 Geometric and Semimodular Lattices Background 265 Reprinted Papers Dependence Relations in a Semi-modular Lattice 269 A Counterexample to the Generalization of Spemer's Theorem 283 (with C. Greene) Articles U. Faigle Dilworth's Completion, Submodular Functions, and 287 Combinatorial Optimiiation J. Kung Dilworth Truncations of Geometric Lattices 295 J.

Inhalt
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.