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Commutative Algebra: Constructive Methods

Finite Projective Modules

  • Henri Lombardi
  • Claude Quitté

Part of the Algebra and Applications book series (AA, volume 20)

Table of contents

  1. Front Matter
    Pages i-xlix
  2. Henri Lombardi, Claude Quitté
    Pages 1-14
  3. Henri Lombardi, Claude Quitté
    Pages 15-75
  4. Henri Lombardi, Claude Quitté
    Pages 77-172
  5. Henri Lombardi, Claude Quitté
    Pages 173-238
  6. Henri Lombardi, Claude Quitté
    Pages 239-293
  7. Henri Lombardi, Claude Quitté
    Pages 295-377
  8. Henri Lombardi, Claude Quitté
    Pages 379-434
  9. Henri Lombardi, Claude Quitté
    Pages 435-475
  10. Henri Lombardi, Claude Quitté
    Pages 477-522
  11. Henri Lombardi, Claude Quitté
    Pages 523-608
  12. Henri Lombardi, Claude Quitté
    Pages 609-668
  13. Henri Lombardi, Claude Quitté
    Pages 669-733
  14. Henri Lombardi, Claude Quitté
    Pages 735-795
  15. Henri Lombardi, Claude Quitté
    Pages 797-833
  16. Henri Lombardi, Claude Quitté
    Pages 835-884
  17. Henri Lombardi, Claude Quitté
    Pages 885-928
  18. Henri Lombardi, Claude Quitté
    Pages 929-945
  19. Back Matter
    Pages 947-996

About this book

Introduction

Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative.

The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century.

This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors, and theoretical computer scientists.

Keywords

Commutative Algebra Constructive Methods Dedekind-Mertens Lemma Finitely Generated Projective Modules Kronecker Theorem Local-Global Principles

Authors and affiliations

  • Henri Lombardi
    • 1
  • Claude Quitté
    • 2
  1. 1.University of Franche-ComtéBesançonFrance
  2. 2.University of PoitiersPoitiersFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-9944-7
  • Copyright Information Springer Science+Business Media Dordrecht 2015
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-94-017-9943-0
  • Online ISBN 978-94-017-9944-7
  • Series Print ISSN 1572-5553
  • Series Online ISSN 2192-2950
  • Buy this book on publisher's site