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978-3-319-03212-2
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9783319032122
978-3-319-03212-2
10.1007/978-3-319-03212-2
doi
QA251.3
PBF
bicssc
MAT002010
bisacsh
512.44
23
Knebusch, Manfred.
author.
Manis Valuations and Prüfer Extensions II
[electronic resource] /
by Manfred Knebusch, Tobias Kaiser.
Cham :
Springer International Publishing :
Imprint: Springer,
2014.
XII, 190 p.
online resource.
text
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rdacontent
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rdamedia
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Lecture Notes in Mathematics,
0075-8434 ;
2103
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.
Mathematics.
Algebra.
Mathematics.
Commutative Rings and Algebras.
Kaiser, Tobias.
author.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9783319032115
Lecture Notes in Mathematics,
0075-8434 ;
2103
http://dx.doi.org/10.1007/978-3-319-03212-2
ZDB-2-SMA
ZDB-2-LNM
Mathematics and Statistics (Springer-11649)
6957
6957
0
0
0
0
18520
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