Manis Valuations and Prüfer Extensions II
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- Synopsis
- 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.
- Copyright:
- 2014
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9783319032122
- Publisher:
- Springer International Publishing, Cham
- Date of Addition:
- 10/21/16
- Copyrighted By:
- Springer
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.