Manis Valuations and Prüfer Extensions II - Couverture souple

Knebusch, Manfred; Kaiser, Tobias

Couverture souple

ISBN 10 : 3319032119 ISBN 13 : 9783319032115

Editeur : Springer, 2014

Synopsis

This volume is a sequel to “Manis Valuation and Prüfer Extensions I,” LNM1791. The Prüfer extensions of a commutative ring A are roughly those commutative ring extensions R / A, where commutative algebra is governed by Manis valuations on R with integral values on A. These valuations then turn out to belong to the particularly amenable subclass of PM (=Prüfer-Manis) valuations. While in Volume I Prüfer extensions in general and individual PM valuations were studied, now the focus is on families of PM valuations. One highlight is the presentation of a very general and deep approximation theorem for PM valuations, going back to Joachim Gräter’s work in 1980, a far-reaching extension of the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called “Kronecker extensions,” where PM valuations are put to use in arbitrary commutative ring extensions in a way that ultimately goes back to the work of Leopold Kronecker.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2014
• Langue: anglais
• ISBN 10: 3319032119
• ISBN 13: 9783319032115
• Reliure: Broché
• Nombre de pages: 204
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne