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Lattice-Ordered Groups

An Introduction

  • Marlow Anderson
  • Todd Feil

Part of the Reidel Texts in the Mathematical Sciences book series (RTMS, volume 4)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Marlow Anderson, Todd Feil
    Pages 1-14
  3. Marlow Anderson, Todd Feil
    Pages 15-20
  4. Marlow Anderson, Todd Feil
    Pages 21-25
  5. Marlow Anderson, Todd Feil
    Pages 26-31
  6. Marlow Anderson, Todd Feil
    Pages 32-37
  7. Marlow Anderson, Todd Feil
    Pages 38-46
  8. Marlow Anderson, Todd Feil
    Pages 47-63
  9. Marlow Anderson, Todd Feil
    Pages 64-76
  10. Marlow Anderson, Todd Feil
    Pages 77-85
  11. Marlow Anderson, Todd Feil
    Pages 86-101
  12. Marlow Anderson, Todd Feil
    Pages 102-108
  13. Back Matter
    Pages 109-190

About this book

Introduction

The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].

Keywords

Finite Morphism function theorem

Authors and affiliations

  • Marlow Anderson
    • 1
  • Todd Feil
    • 2
  1. 1.The Colorado CollegeColorado SpringsUSA
  2. 2.Department of Mathematical SciencesDenison UniversityGranvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-2871-8
  • Copyright Information Springer Science+Business Media B.V. 1988
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-7792-7
  • Online ISBN 978-94-009-2871-8
  • Series Print ISSN 0921-9315
  • Buy this book on publisher's site
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