Description |
1 online resource (xii, 190 pages) |
Series |
Lecture notes in mathematics, 0075-8434 ; 2103 |
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Lecture notes in mathematics (Springer-Verlag) ; 2103.
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Contents |
Overrings and PM-Spectra -- Approximation theorems -- Kronecker extensions and Star operations |
Summary |
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 |
Notes |
Continuation of: Manis valuations and Prüfer extensions I (Lecture notes in mathematics (Springer-Verlag); 1791) |
Bibliography |
Includes bibliographical references (pages 181-182) and indexes |
Notes |
Print version record |
Subject |
Prüfer rings.
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Commutative rings.
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Commutative algebra.
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Approximation theory.
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Approximation theory
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Commutative algebra
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Commutative rings
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Prüfer rings
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Form |
Electronic book
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Author |
Kaiser, Tobias, 1975-
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ISBN |
9783319032122 |
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3319032127 |
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