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Lattice Concepts of Module Theory

  • Grigore Călugăreanu

Part of the Springer Texts in the Mathematical Sciences book series (TMS, volume 22)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Grigore Călugăreanu
    Pages 1-16
  3. Grigore Călugăreanu
    Pages 17-27
  4. Grigore Călugăreanu
    Pages 29-38
  5. Grigore Călugăreanu
    Pages 39-45
  6. Grigore Călugăreanu
    Pages 47-58
  7. Grigore Călugăreanu
    Pages 59-75
  8. Grigore Călugăreanu
    Pages 77-86
  9. Grigore Călugăreanu
    Pages 87-98
  10. Grigore Călugăreanu
    Pages 99-114
  11. Grigore Călugăreanu
    Pages 115-122
  12. Grigore Călugăreanu
    Pages 123-129
  13. Grigore Călugăreanu
    Pages 131-142
  14. Grigore Călugăreanu
    Pages 143-163
  15. Grigore Călugăreanu
    Pages 165-218
  16. Back Matter
    Pages 219-225

About this book

Introduction

It became more and more usual, from, say, the 1970s, for each book on Module Theory, to point out and prove some (but in no more than 15 to 20 pages) generalizations to (mostly modular) lattices. This was justified by the nowadays widely accepted perception that the structure of a module over a ring is best understood in terms of the lattice struc­ ture of its submodule lattice. Citing Louis H. Rowen "this important example (the lattice of all the submodules of a module) is the raison d'etre for the study of lattice theory by ring theorists". Indeed, many module-theoretic results can be proved by using lattice theory alone. The purpose of this book is to collect and present all and only the results of this kind, although for this purpose one must develop some significant lattice theory. The results in this book are of the following categories: the folklore of Lattice Theory (to be found in each Lattice Theory book), module­ theoretic results generalized in (modular, and possibly compactly gen­ erated) lattices (to be found in some 6 to 7 books published in the last 20 years), very special module-theoretic results generalized in lattices (e. g. , purity in Chapter 9 and several dimensions in Chapter 13, to be found mostly in [27], respectively, [34] and [18]) and some new con­ cepts (e. g.

Keywords

Group theory Lattice algebra torsion

Authors and affiliations

  • Grigore Călugăreanu
    • 1
  1. 1.Department of Algebra, Faculty of Mathematics and Computer SciencesBabeş-Bolyai UniversityCluj-NapocaRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9588-9
  • Copyright Information Springer Science+Business Media B.V. 2000
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5530-9
  • Online ISBN 978-94-015-9588-9
  • Series Print ISSN 0927-4529
  • Buy this book on publisher's site
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