Manis Valuations and Prüfer Extensions I [electronic resource] : A New Chapter in Commutative Algebra / by Manfred Knebusch, Digen Zhang.
Material type: TextSeries: Lecture Notes in Mathematics ; 1791Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002Description: CCLXXXIV, 274 p. online resourceContent type:- text
- computer
- online resource
- 9783540456254
- 512.44 23
- QA251.3
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.
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.
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