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Manis Valuations and Prüfer Extensions I

A New Chapter in Commutative Algebra

  • Authors
  • Manfred Knebusch
  • Digen Zhang

Part of the Lecture Notes in Mathematics book series (LNM, volume 1791)

Table of contents

  1. Front Matter
    Pages N2-VI
  2. Manfred Knebusch, Digen Zhang
    Pages 1-6
  3. Manfred Knebusch, Digen Zhang
    Pages 7-7
  4. Manfred Knebusch, Digen Zhang
    Pages 9-81
  5. Manfred Knebusch, Digen Zhang
    Pages 83-176
  6. Manfred Knebusch, Digen Zhang
    Pages 177-250
  7. Manfred Knebusch, Digen Zhang
    Pages 251-256
  8. Manfred Knebusch, Digen Zhang
    Pages 257-262
  9. Manfred Knebusch, Digen Zhang
    Pages 263-267
  10. Back Matter
    Pages 269-271

About this book

Introduction

The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter.

Keywords

Bezout ring Manis valuation Prüfer ring Volume holormorphy ring multiplicative ideal theory

Bibliographic information

  • DOI https://doi.org/10.1007/b84018
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43951-6
  • Online ISBN 978-3-540-45625-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site