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

Demtroder, W.

ISBN 10: 354043951X / ISBN 13: 9783540439516

Editore: Springer 2002-08, 2002

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Codice articolo 6666-IUK-9783540439516

Dati bibliografici

• Titolo: Manis Valuations and PR Fer Extensions I: A New Chapter in Commutative Algebra
• Editore: Springer 2002-08
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 354043951X
• ISBN 13: 9783540439516
• Rilegatura: PF
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

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.