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

ISBN-13: 9783540439516 / Angielski / Miękka / 2002 / 274 str.

W. Demtroder; M. Knebusch; D. Zhang

Opis

The present book is devoted to a study of relative Prufer 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.

Spis treści

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.