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

• Main Authors: Knebusch, Manfred (Author, http://id.loc.gov/vocabulary/relators/aut), Zhang, Digen (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1791
• Subjects: Commutative algebra.; Commutative rings.; Algebraic geometry.; Commutative Rings and Algebras.; Algebraic Geometry.

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 t...

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.