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AuthorKnebusch, Manfred. author
TitleManis Valuations and Prรผfer Extensions I [electronic resource] : A New Chapter in Commutative Algebra / by Manfred Knebusch, Digen Zhang
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2002
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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

Mathematics Algebraic geometry Commutative algebra Commutative rings Mathematics Commutative Rings and Algebras Algebraic Geometry


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