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.
| Autorius: | Tobias Kaiser, Manfred Knebusch, |
| Serija: | Lecture Notes in Mathematics |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2014 |
| Knygos puslapių skaičius: | 204 |
| ISBN-10: | 3319032119 |
| ISBN-13: | 9783319032115 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Algebra |
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