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Rings and Geometry

  • Rüstem Kaya
  • Peter Plaumann
  • Karl Strambach

Part of the NATO ASI Series book series (ASIC, volume 160)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Non-Commutative Algebraic Geometry

  3. Hjelmslev Geometries

    1. Front Matter
      Pages 79-79
    2. David A. Drake, Dieter Jungnickel
      Pages 153-231
  4. Geometries over Alternative Rings

    1. Front Matter
      Pages 233-233
    2. John R. Faulkner, Joseph C. Ferrar
      Pages 235-288
    3. Ferdinand D. Veldkamp
      Pages 289-350
  5. Metric Ring Geometries, Linear Groups over Rings and Coordinatization

    1. Front Matter
      Pages 351-351
    2. Claudio Bartolone, Federico Bartolozzi
      Pages 353-389
    3. Bernard R. McDonald
      Pages 391-415
    4. Bernard R. McDonald
      Pages 417-436
    5. Helmut Karzel, Günter Kist
      Pages 437-509
    6. Ulrich Brehm
      Pages 511-550
  6. Epilog

    1. Front Matter
      Pages 551-551
  7. Back Matter
    Pages 557-567

About this book

Introduction

When looking for applications of ring theory in geometry, one first thinks of algebraic geometry, which sometimes may even be interpreted as the concrete side of commutative algebra. However, this highly de­ veloped branch of mathematics has been dealt with in a variety of mono­ graphs, so that - in spite of its technical complexity - it can be regarded as relatively well accessible. While in the last 120 years algebraic geometry has again and again attracted concentrated interes- which right now has reached a peak once more - , the numerous other applications of ring theory in geometry have not been assembled in a textbook and are scattered in many papers throughout the literature, which makes it hard for them to emerge from the shadow of the brilliant theory of algebraic geometry. It is the aim of these proceedings to give a unifying presentation of those geometrical applications of ring theo~y outside of algebraic geometry, and to show that they offer a considerable wealth of beauti­ ful ideas, too. Furthermore it becomes apparent that there are natural connections to many branches of modern mathematics, e. g. to the theory of (algebraic) groups and of Jordan algebras, and to combinatorics. To make these remarks more precise, we will now give a description of the contents. In the first chapter, an approach towards a theory of non-commutative algebraic geometry is attempted from two different points of view.

Keywords

algebra algebraic geometry commutative algebra homomorphism linear algebra matrices matrix quadratic form

Editors and affiliations

  • Rüstem Kaya
    • 1
  • Peter Plaumann
    • 2
  • Karl Strambach
    • 2
  1. 1.Graduate School of SciencesUniversity of AnadoluEskisehirTurkey
  2. 2.Mathematical InstituteUniversity Erlangen-NürnbergErlangenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-5460-1
  • Copyright Information Springer Science+Business Media B.V. 1985
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-8911-1
  • Online ISBN 978-94-009-5460-1
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site
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