Author	Knebusch, Manfred. author
Title	Manis Valuations and Prรผfer Extensions I [electronic resource] : A New Chapter in Commutative Algebra / by Manfred Knebusch, Digen Zhang
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2002
Connect to	http://dx.doi.org/10.1007/b84018
Descript	CCLXXXIV, 274 p. online resource

The present book is devoted to a study of relative Prรผfer 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 Prรผfer 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

1. Mathematics
2. Algebraic geometry
3. Commutative algebra
4. Commutative rings
5. Mathematics
6. Commutative Rings and Algebras
7. Algebraic Geometry