Manis Valuations and Prüfer Extensions II
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...
| Published in: | Springer eBooks |
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| Format: | eBook |
| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2014.
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| Series: | Lecture Notes in Mathematics,
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| Online Access: | http://dx.doi.org/10.1007/978-3-319-03212-2 Перейти в каталог НБ ТГУ |
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| 039 | 9 | |y 201609152152 |z Александр Эльверович Гилязов | |
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| 100 | 1 | |a Knebusch, Manfred. |e author. |9 448444 | |
| 245 | 1 | 0 | |a Manis Valuations and Prüfer Extensions II |h electronic resource |c by Manfred Knebusch, Tobias Kaiser. |
| 260 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2014. |9 742221 | ||
| 300 | |a XII, 190 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 0075-8434 ; |v 2103 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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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| 650 | 0 | |a Algebra. |9 281363 | |
| 650 | 1 | 4 | |a Mathematics. |9 566184 |
| 650 | 2 | 4 | |a Commutative Rings and Algebras. |9 303210 |
| 700 | 1 | |a Kaiser, Tobias. |e author. |9 448445 | |
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| 856 | 4 | 0 | |u http://dx.doi.org/10.1007/978-3-319-03212-2 |
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