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The Dilworth Theorems

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Cover of 'The Dilworth Theorems'

Table of Contents

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    Book Overview
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    Chapter 1 A Decomposition Theorem for Partially Ordered Sets
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    Chapter 2 Some Combinatorial Problems on Partially Ordered Sets
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    Chapter 3 The Impact of the Chain Decomposition Theorem on Classical Combinatorics
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    Chapter 4 Dilworth’s Decomposition Theorem in the Infinite Case
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    Chapter 5 Effective Versions of the Chain Decomposition Theorem
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    Chapter 6 Lattices with Unique Complements
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    Chapter 7 On Complemented Lattices
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    Chapter 8 Uniquely Complemented Lattices
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    Chapter 9 On Orthomodular Lattices
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    Chapter 10 Lattices with Unique Irreducible Decompositions
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    Chapter 11 The Arithmetical Theory of Birkhoff Lattices
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    Chapter 12 Ideals in Birkhoff Lattices
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    Chapter 13 Decomposition Theory for Lattices without Chain Conditions
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    Chapter 14 Note on the Kurosch-Ore Theorem
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    Chapter 15 Structure and Decomposition Theory of Lattices
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    Chapter 16 Dilworth’s Work on Decompositions in Semimodular Lattices
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    Chapter 17 The Consequences of Dilworth’s Work on Lattices with Unique Irreducible Decompositions
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    Chapter 18 Exchange Properties for Reduced Decompositions in Modular Lattices
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    Chapter 19 The Impact of Dilworth’s Work on Semimodular Lattices on the Kurosch-Ore Theorem
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    Chapter 20 The Imbedding Problem for Modular Lattices
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    Chapter 21 Proof of a Conjecture on Finite Modular Lattices
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    Chapter 22 Distributivity in Lattices
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    Chapter 23 Aspects of distributivity
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    Chapter 24 The Role of Gluing Constructions in Modular Lattice Theory
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    Chapter 25 Dilworth’s Covering Theorem for Modular Lattices
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    Chapter 26 Dependence Relations in a Semi-Modular Lattice
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    Chapter 27 A Counterexample to the Generalization of Sperner’s Theorem
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    Chapter 28 Dilworth’s Completion, Submodular Functions, and Combinatorial Optimization
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    Chapter 29 Dilworth Truncations of Geometric Lattices
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    Chapter 30 The Sperner Property in Geometric and Partition Lattices
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    Chapter 31 Abstract Residuation over Lattices
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    Chapter 32 Residuated Lattices
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    Chapter 33 Non-Commutative Residuated Lattices
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    Chapter 34 Non-Commutative Arithmetic
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    Chapter 35 Abstract Commutative Ideal Theory
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    Chapter 36 Dilworth’s Early Papers on Residuated and Multiplicative Lattices
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    Chapter 37 Abstract Ideal Theory: Principals and Particulars
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    Chapter 38 Representation and Embedding Theorems for Noether Lattices and r -Lattices
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    Chapter 39 The Structure of Relatively Complemented Lattices
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    Chapter 40 The Normal Completion of the Lattice of Continuous Functions
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    Chapter 41 A Generalized Cantor Theorem
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    Chapter 42 Generators of lattice varieties
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    Chapter 43 Lattice Congruences and Dilworth’s Decomposition of Relatively Complemented Lattices
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    Chapter 44 The Normal Completion of the Lattice of Continuous Functions
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    Chapter 45 Cantor Theorems for Relations
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    Chapter 46 Ideal and Filter Constructions in Lattice Varieties
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    Chapter 47 Dilworth’s Proof of the Embedding Theorem
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    Chapter 48 On the Congruence Lattice of a Lattice
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Title
The Dilworth Theorems
Published by
Birkhäuser Boston, November 2013
DOI 10.1007/978-1-4899-3558-8
ISBNs
978-1-4899-3560-1, 978-1-4899-3558-8
Editors

Bogart, Kenneth P., Freese, Ralph, Kung, Joseph P. S.

Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 4 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
India 1 25%
Unknown 3 75%

Demographic breakdown

Readers by professional status Count As %
Professor 1 25%
Student > Ph. D. Student 1 25%
Professor > Associate Professor 1 25%
Researcher 1 25%
Readers by discipline Count As %
Mathematics 3 75%
Agricultural and Biological Sciences 1 25%