Manis Valuations and Prüfer Extensions I

A New Chapter in Commutative Algebra
2002
ISBN: 978-3-540-43951-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1791, 274 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 410 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Zhang, Digen

Knebusch, Manfred

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.