Manis Valuations and Prüfer Extensions I: A New Chapter in Commutative Algebra

by Manfred Knebusch, Digen Zhang

Overview

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

ISBN-13:	9783540439516
Publisher:	Springer Berlin Heidelberg
Publication date:	10/03/2002
Series:	Lecture Notes in Mathematics , #1791
Edition description:	2002
Pages:	274
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table 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.