Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2103)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Manis Valuations and Prüfer Extensions II
Authors: Manfred Knebusch, Tobias Kaiser
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-03212-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2014
Softcover ISBN: 978-3-319-03211-5Published: 02 April 2014
eBook ISBN: 978-3-319-03212-2Published: 20 March 2014
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 190
Topics: Commutative Rings and Algebras