EAN: 9783319032115

Bilder-Quelle: discount24.de - Sport-Freizeit

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.

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