Manis Valuations and Prüfer Extensions I

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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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.

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

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