Manis Valuations and Prufer Extensions II

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Opis: Manis Valuations and Prufer Extensions II - Manfred Knebusch, Tobias Kaiser

This volume is a sequel to "Manis Valuation and Prufer Extensions I," LNM1791. The Prufer 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 (=Prufer-Manis) valuations. While in Volume I Prufer 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 Grater'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.Overrings and PM-Spectra.- Approximation Theorems.- Kronecker extensions and star operations.- Basics on Manis valuations and Prufer extensions.- Multiplicative ideal theory.- PM-valuations and valuations of weaker type.- Overrings and PM-Spectra.- Approximation Theorems.- Kronecker extensions and star operations.- Appendix.- References.- Index.


Szczegóły: Manis Valuations and Prufer Extensions II - Manfred Knebusch, Tobias Kaiser

Tytuł: Manis Valuations and Prufer Extensions II
Autor: Manfred Knebusch, Tobias Kaiser
Producent: Springer Verlag
ISBN: 9783319032115
Rok produkcji: 2014
Ilość stron: 202
Oprawa: Miękka
Waga: 0.32 kg


Recenzje: Manis Valuations and Prufer Extensions II - Manfred Knebusch, Tobias Kaiser

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Manis Valuations and Prufer Extensions II

,

This volume is a sequel to "Manis Valuation and Prufer Extensions I," LNM1791. The Prufer 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 (=Prufer-Manis) valuations. While in Volume I Prufer 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 Grater'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.Overrings and PM-Spectra.- Approximation Theorems.- Kronecker extensions and star operations.- Basics on Manis valuations and Prufer extensions.- Multiplicative ideal theory.- PM-valuations and valuations of weaker type.- Overrings and PM-Spectra.- Approximation Theorems.- Kronecker extensions and star operations.- Appendix.- References.- Index.

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Cena 154,00 PLN
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Szczegóły: Manis Valuations and Prufer Extensions II - Manfred Knebusch, Tobias Kaiser

Tytuł: Manis Valuations and Prufer Extensions II
Autor: Manfred Knebusch, Tobias Kaiser
Producent: Springer Verlag
ISBN: 9783319032115
Rok produkcji: 2014
Ilość stron: 202
Oprawa: Miękka
Waga: 0.32 kg


Recenzje: Manis Valuations and Prufer Extensions II - Manfred Knebusch, Tobias Kaiser

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