Manfred Knebusch, Digen Zhang

Manis Valuations and Prüfer Extensions I (eBook, PDF)

A New Chapter in Commutative Algebra

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 274
• Erscheinungstermin: 19. Oktober 2004
• Englisch
• ISBN-13: 9783540456254
• Artikelnr.: 53392332

Autorenporträt

Manfred Knebusch, University of Regensburg, Germany / Digen Zhang, University of Regensburg, Germany

Inhaltsangabe

- Introduction
- Basics on Manis valuations and Prüfer extensions
- Multiplicative ideal theory
- PM-valuations and valuations of weaker type
- Appendix A: Flat epimorphisms
- Appendix B: Arithmetical rings
- Appendix C: A direct proof of the existence of Manis valuation hulls
- References
- Index.