Hidden Bibliographic Details
| Other authors / contributors: | Kaiser, Tobias, 1975-
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| ISBN: | 9783319032122
3319032127
9783319032115
3319032119
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| Digital file characteristics: | text file PDF
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| Notes: | Continuation of: Manis valuations and Prüfer extensions I (Lecture notes in mathematics (Springer-Verlag) ; 1791).
Includes bibliographical references (pages 181-182) and indexes.
Print version record.
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| Summary: | 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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| Other form: | Print version: Knebusch, Manfred. Manis valuations and Prüfer extensions II 3319032119
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| Standard no.: | 10.1007/978-3-319-03212-2
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