Determinantal Rings

  • Authors
  • Winfried Bruns
  • Udo Vetter

Part of the Lecture Notes in Mathematics book series (LNM, volume 1327)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Winfried Bruns, Udo Vetter
    Pages 1-9
  3. Winfried Bruns, Udo Vetter
    Pages 10-26
  4. Winfried Bruns, Udo Vetter
    Pages 27-37
  5. Winfried Bruns, Udo Vetter
    Pages 38-49
  6. Winfried Bruns, Udo Vetter
    Pages 50-63
  7. Winfried Bruns, Udo Vetter
    Pages 64-72
  8. Winfried Bruns, Udo Vetter
    Pages 73-92
  9. Winfried Bruns, Udo Vetter
    Pages 93-104
  10. Winfried Bruns, Udo Vetter
    Pages 105-121
  11. Winfried Bruns, Udo Vetter
    Pages 122-134
  12. Winfried Bruns, Udo Vetter
    Pages 135-152
  13. Winfried Bruns, Udo Vetter
    Pages 153-161
  14. Winfried Bruns, Udo Vetter
    Pages 162-173
  15. Winfried Bruns, Udo Vetter
    Pages 174-183
  16. Winfried Bruns, Udo Vetter
    Pages 184-201
  17. Winfried Bruns, Udo Vetter
    Pages 202-218
  18. Back Matter
    Pages 219-238

About this book

Introduction

Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.

Keywords

algebra commutative algebra commutative ring representation theory ring theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0080378
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19468-2
  • Online ISBN 978-3-540-39274-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book