Manis Valuations and Prüfer Extensions I

A New Chapter in Commutative Algebra

Manfred Knebusch, Digen Zhang (Autoren)

Buch | Softcover

CCLXXXIV, 274 Seiten

2002
Springer Berlin (Verlag)
978-3-540-43951-6 (ISBN)

Artikel merken

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.

- 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.

Erscheint lt. Verlag	20.8.2002
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	CCLXXXIV, 274 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	420 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Bezout ring • holormorphy ring • Kommutative Algebra • Manis valuation • multiplicative ideal theory • Prüfer ring • Volume
ISBN-10	3-540-43951-X / 354043951X
ISBN-13	978-3-540-43951-6 / 9783540439516
Zustand	Neuware