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Rings and Geometry

  • Book
  • © 1985

Overview

Editors:
  1. Rüstem Kaya

    1. Graduate School of Sciences, University of Anadolu, Eskisehir, Turkey

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    You can also search for this editor in PubMed   Google Scholar

  2. Peter Plaumann

    1. Mathematical Institute, University Erlangen-Nürnberg, Erlangen, Germany

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    You can also search for this editor in PubMed   Google Scholar

  3. Karl Strambach

    1. Mathematical Institute, University Erlangen-Nürnberg, Erlangen, Germany

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nato Science Series C: (ASIC, volume 160)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. Non-Commutative Algebraic Geometry

    1. Front Matter

      Pages 1-1
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    2. Principles of Non-Commutative Algebraic Geometry

      • P. M. Cohn
      Pages 3-37

    3. Applications of Results on Generalized Polynomial Identities in Desarguesian Projective Spaces

      • Hans Havlicek
      Pages 39-77

  3. Hjelmslev Geometries

    1. Front Matter

      Pages 79-79
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    2. A Topological Characterization of Hjelmslev’s Classical Geometries

      • J. W. Lorimer
      Pages 81-151

    3. Finite Hjelmslev Planes and Klingenberg Epimorphisms

      • David A. Drake, Dieter Jungnickel
      Pages 153-231

  4. Geometries over Alternative Rings

    1. Front Matter

      Pages 233-233
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    2. Generalizing the Moufang Plane

      • John R. Faulkner, Joseph C. Ferrar
      Pages 235-288

    3. Projective Ring Planes and Their Homomorphisms

      • Ferdinand D. Veldkamp
      Pages 289-350

  5. Metric Ring Geometries, Linear Groups over Rings and Coordinatization

    1. Front Matter

      Pages 351-351
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    2. Topics in Geometric Algebra over Rings

      • Claudio Bartolone, Federico Bartolozzi
      Pages 353-389

    3. Metric Geometry over Local-Global Commutative Rings

      • Bernard R. McDonald
      Pages 391-415

    4. Linear Mappings of Matrix Rings Preserving Invariants

      • Bernard R. McDonald
      Pages 417-436

    5. Kinematic Algebras and Their Geometries

      • Helmut Karzel, Günter Kist
      Pages 437-509

    6. Coordinatization of Lattices

      • Ulrich Brehm
      Pages 511-550

  6. Epilog

    1. Front Matter

      Pages 551-551
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    2. The Advantage of Geometric Concepts in Mathematics

      • C. Arf
      Pages 553-556

  7. Back Matter

    Pages 557-567
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Keywords

About this book

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.

Editors and Affiliations

  • Graduate School of Sciences, University of Anadolu, Eskisehir, Turkey

    Rüstem Kaya

  • Mathematical Institute, University Erlangen-Nürnberg, Erlangen, Germany

    Peter Plaumann, Karl Strambach

Bibliographic Information

  • Book Title: Rings and Geometry

  • Editors: Rüstem Kaya, Peter Plaumann, Karl Strambach

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-009-5460-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company 1985

  • Hardcover ISBN: 978-90-277-2112-9Published: 30 September 1985

  • Softcover ISBN: 978-94-010-8911-1Published: 02 October 2011

  • eBook ISBN: 978-94-009-5460-1Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: XII, 568

  • Topics: Algebra

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