Manis Valuations and Prüfer Extensions I. Vol.1 - A New Chapter in Commutative Algebra

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.

List of contents

- 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.

Summary

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.

Product details

• Authors: M. Knebusch, Manfre Knebusch, Manfred Knebusch, D. Zhang, Digen Zhang
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 07.10.2002
• EAN: 9783540439516
• ISBN: 978-3-540-43951-6
• No. of pages: 274
• Dimensions: 146 mm x 229 mm x 16 mm
• Weight: 416 g
• Illustrations: CCLXXXIV, 274 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; B, Algebraische Geometrie, Mathematics and Statistics, Algebraic Geometry, Commutative algebra, Commutative rings, Commutative Rings and Algebras