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Birkhäuser

The Dilworth Theorems

Selected Papers of Robert P. Dilworth

  • Book
  • © 1990

Overview

Editors:
  1. Kenneth P. Bogart

    1. Department of Mathematics and Computer Science, Dartmouth College, Hanover, USA

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  2. Ralph Freese

    1. Department of Mathematics, University of Hawaii, Honolulu, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Joseph P. S. Kung

    1. Department of Mathematics, University of North Texas, Denton, USA

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Part of the book series: Contemporary Mathematicians (CM)

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Table of contents (48 chapters)

  1. Front Matter

    Pages i-xxvi
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  2. Chain Partitions in Ordered Sets

    1. Front Matter

      Pages 1-6
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    2. Reprinted Papers

      1. A Decomposition Theorem for Partially Ordered Sets
        • R. P. Dilworth
        Pages 7-12
      2. Some Combinatorial Problems on Partially Ordered Sets
        • R. P. Dilworth
        Pages 13-18

    3. Articles

      1. The Impact of the Chain Decomposition Theorem on Classical Combinatorics
        • Kenneth P. Bogart, Curtis Greene, Joseph P. S. Kung
        Pages 19-29
      2. Dilworth’s Decomposition Theorem in the Infinite Case
        • E. C. Milner
        Pages 30-35
      3. Effective Versions of the Chain Decomposition Theorem
        • H. Kierstead
        Pages 36-38

  3. Complementation

    1. Front Matter

      Pages 39-40
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    2. Reprinted Papers

      1. Lattices with Unique Complements
        • R. P. Dilworth
        Pages 41-72
      2. On Complemented Lattices
        • R. P. Dilworth
        Pages 73-78

    3. Articles

      1. Uniquely Complemented Lattices
        • M. E. Adams
        Pages 79-84
      2. On Orthomodular Lattices
        • Gudrun Kalmbach
        Pages 85-87

  4. Decomposition Theory

    1. Front Matter

      Pages 89-92
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    2. Reprinted Papers

      1. Lattices with Unique Irreducible Decompositions
        • R. P. Dilworth
        Pages 93-99
      2. The Arithmetical Theory of Birkhoff Lattices
        • R. P. Dilworth
        Pages 101-114
      3. Ideals in Birkhoff Lattices
        • R. P. Dilworth
        Pages 115-143
      4. Decomposition Theory for Lattices without Chain Conditions
        • R. P. Dilworth, Peter Crawley
        Pages 145-166
      5. Note on the Kurosch-Ore Theorem
        • R. P. Dilworth
        Pages 167-171
      6. Structure and Decomposition Theory of Lattices
        • R. P. Dilworth
        Pages 173-186

    3. Articles

      1. Dilworth’s Work on Decompositions in Semimodular Lattices
        • Bjarni Jónsson
        Pages 187-191
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Keywords

Editors and Affiliations

  • Department of Mathematics and Computer Science, Dartmouth College, Hanover, USA

    Kenneth P. Bogart

  • Department of Mathematics, University of Hawaii, Honolulu, USA

    Ralph Freese

  • Department of Mathematics, University of North Texas, Denton, USA

    Joseph P. S. Kung

Bibliographic Information

  • Book Title: The Dilworth Theorems

  • Book Subtitle: Selected Papers of Robert P. Dilworth

  • Editors: Kenneth P. Bogart, Ralph Freese, Joseph P. S. Kung

  • Series Title: Contemporary Mathematicians

  • DOI: https://doi.org/10.1007/978-1-4899-3558-8

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1990

  • Softcover ISBN: 978-1-4899-3560-1Published: 30 July 2013

  • eBook ISBN: 978-1-4899-3558-8Published: 22 November 2013

  • Series ISSN: 0884-7037

  • Edition Number: 1

  • Number of Pages: XXVI, 465

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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