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Manis Valuations and Prüfer Extensions I

A New Chapter in Commutative Algebra

  • Book
  • © 2002

Overview

Authors:
  1. Manfred Knebusch
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  2. Digen Zhang
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1791)

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Table of contents (8 chapters)

  1. Front Matter

    Pages N2-VI
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  2. Introduction

    • Manfred Knebusch, Digen Zhang
    Pages 1-6

  3. Summary

    • Manfred Knebusch, Digen Zhang
    Pages 7-7

  4. Chapter I: Basics on Manis valuations and Prüfer extensions

    • Manfred Knebusch, Digen Zhang
    Pages 9-81

  5. Chapter II: Multiplicative ideal theory

    • Manfred Knebusch, Digen Zhang
    Pages 83-176

  6. Chapter III: PM-valuations and valuations of weaker type

    • Manfred Knebusch, Digen Zhang
    Pages 177-250

  7. Appendix

    • Manfred Knebusch, Digen Zhang
    Pages 251-256

  8. References

    • Manfred Knebusch, Digen Zhang
    Pages 257-262

  9. Subject and Symbol Index

    • Manfred Knebusch, Digen Zhang
    Pages 263-267

  10. Back Matter

    Pages 269-271
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Manis Valuations and Prüfer Extensions I

  • Book Subtitle: A New Chapter in Commutative Algebra

  • Authors: Manfred Knebusch, Digen Zhang

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b84018

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-43951-6Published: 20 August 2002

  • eBook ISBN: 978-3-540-45625-4Published: 19 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: CCLXXXIV, 274

  • Topics: Commutative Rings and Algebras, Algebraic Geometry

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