9783319032115 - Manis Valuations and Prüfer Extensions II (Lecture Notes in Mathematics, Band 2103) von Knebusch, Manfred; Kaiser, Tobias (4 Ergebnisse)

Kartoniert / Broschiert. Zustand: New.

Paperback. Zustand: Brand New. 2014 edition. 190 pages. 9.00x6.00x0.50 inches. In Stock.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.

Zustand: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | 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.