UID:
almahu_9947363761502882
Format:
XII, 190 p.
,
online resource.
ISBN:
9783319032122
Series Statement:
Lecture Notes in Mathematics, 2103
Content:
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.
Note:
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.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783319032115
Language:
English
Subjects:
Mathematics
DOI:
10.1007/978-3-319-03212-2
URL:
http://dx.doi.org/10.1007/978-3-319-03212-2
URL:
Volltext
(lizenzpflichtig)
