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TitleThe Dilworth Theorems [electronic resource] : Selected Papers of Robert P. Dilworth / edited by Kenneth P. Bogart, Ralph Freese, Joseph P. S. Kung
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1990
Connect tohttp://dx.doi.org/10.1007/978-1-4899-3558-8
Descript XXVI, 465 p. 2 illus. online resource

CONTENT

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 -- Dilworthโ{128}{153}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 -- Dilworthโ{128}{153}s Work on Decompositions in Semimodular Lattices -- The Consequences of Dilworthโ{128}{153}s Work on Lattices with Unique Irreducible Decompositions -- Exchange Properties for Reduced Decompositions in Modular Lattices -- The Impact of Dilworthโ{128}{153}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 -- Dilworthโ{128}{153}s Covering Theorem for Modular Lattices -- Geometric and Semimodular Lattices -- Dependence Relations in a Semi-Modular Lattice -- A Counterexample to the Generalization of Spernerโ{128}{153}s Theorem -- Dilworthโ{128}{153}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 -- Dilworthโ{128}{153}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 Dilworthโ{128}{153}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 โ{128}{156}Algebraic Theory of Latticesโ{128}{157} -- Dilworthโ{128}{153}s Proof of the Embedding Theorem -- On the Congruence Lattice of a Lattice


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