Lattice-ordered Rings and Modules

  • Stuart A.¬†Steinberg

Table of contents

  1. Front Matter
    Pages 1-15
  2. Stuart A. Steinberg
    Pages 1-31
  3. Stuart A. Steinberg
    Pages 33-123
  4. Stuart A. Steinberg
    Pages 125-279
  5. Stuart A. Steinberg
    Pages 281-417
  6. Stuart A. Steinberg
    Pages 419-509
  7. Stuart A. Steinberg
    Pages 511-607
  8. Back Matter
    Pages 1-21

About this book

Introduction

This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the work self-contained and accessible to a variety of readers is included.

Steinberg includes in his presentation of the material 800+ extensive exercises of varying levels of difficulty at the end of each of the sections.  The first two chapters of the book provide a thorough introduction to the material, while the following four chapters delve into more specific topics.

Key topics include:

*lattice-ordered groups, rings, and fields;

*archimedean $l$-groups;

*f-rings and larger varieties of $l$-rings;

*the category of f-modules;

*various commutativity results.

Filling a gap in the literature, Lattice-Ordered Rings and Modules may be used as a textbook or for self-study by graduate students and researchers studying lattice-ordered rings and lattice-ordered modules.

Keywords

Algebra Archimedean f-rings Group theory Hahn products Torsion theories embedding theorem homomorphism lattice-ordered fields lattice-ordered groups lattice-ordered rings partially ordered sets ring theory

Authors and affiliations

  • Stuart A.¬†Steinberg
    • 1
  1. 1.University of ToledoDepartment of MathematicsToledoU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-1721-8
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-1720-1
  • Online ISBN 978-1-4419-1721-8
  • About this book