Manis valuations and Prüfer extensions II /
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| Author / Creator: | Knebusch, Manfred. |
|---|---|
| Imprint: | Cham [Switzerland] : Springer, [2014] ©2014 |
| Description: | 1 online resource (xii, 190 pages). |
| Language: | English |
| Series: | Lecture notes in mathematics, 0075-8434 ; 2103 Lecture notes in mathematics (Springer-Verlag) ; 2103. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11084542 |
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| 100 | 1 | |a Knebusch, Manfred. |0 http://id.loc.gov/authorities/names/n80098078 |1 http://viaf.org/viaf/108261919 | |
| 245 | 1 | 0 | |a Manis valuations and Prüfer extensions II / |c Manfred Knebusch, Tobias Kaiser. |
| 264 | 1 | |a Cham [Switzerland] : |b Springer, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (xii, 190 pages). | ||
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| 490 | 1 | |a Lecture notes in mathematics, |x 0075-8434 ; |v 2103 | |
| 500 | |a Continuation of: Manis valuations and Prüfer extensions I (Lecture notes in mathematics (Springer-Verlag) ; 1791). | ||
| 505 | 0 | |a Overrings and PM-Spectra -- Approximation theorems -- Kronecker extensions and Star operations. | |
| 504 | |a Includes bibliographical references (pages 181-182) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 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. | ||
| 650 | 0 | |a Prüfer rings. |0 http://id.loc.gov/authorities/subjects/sh96007623 | |
| 650 | 0 | |a Commutative rings. |0 http://id.loc.gov/authorities/subjects/sh85029269 | |
| 650 | 0 | |a Commutative algebra. |0 http://id.loc.gov/authorities/subjects/sh85029267 | |
| 650 | 0 | |a Approximation theory. |0 http://id.loc.gov/authorities/subjects/sh85006190 | |
| 650 | 7 | |a Approximation theory. |2 fast |0 (OCoLC)fst00811829 | |
| 650 | 7 | |a Commutative algebra. |2 fast |0 (OCoLC)fst00871202 | |
| 650 | 7 | |a Commutative rings. |2 fast |0 (OCoLC)fst00871205 | |
| 650 | 7 | |a Prüfer rings. |2 fast |0 (OCoLC)fst01080767 | |
| 700 | 1 | |a Kaiser, Tobias, |d 1975- |0 http://id.loc.gov/authorities/names/no2014048375 |1 http://viaf.org/viaf/305432693 | |
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| 830 | 0 | |a Lecture notes in mathematics (Springer-Verlag) ; |v 2103. | |
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