# Manis Valuations and Prüfer Extensions II [electronic resource] / by Manfred Knebusch, Tobias Kaiser.

Series: Lecture Notes in Mathematics ; 2103Publisher: Cham : Springer International Publishing : Imprint: Springer, 2014Description: XII, 190 p. online resourceContent type:- text

- computer

- online resource

- 9783319032122

- 512.44 23

- QA251.3

Item type | Current library | Call number | Status | Date due | Barcode | |
---|---|---|---|---|---|---|

E-Books | Central Library, IISER Bhopal | 512.44 (Browse shelf(Opens below)) | Not for loan |

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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.

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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