| Description |
1 online resource (xii, 190 pages) |
| Series |
Lecture notes in mathematics, 0075-8434 ; 2103 |
|
Lecture notes in mathematics (Springer-Verlag) ; 2103.
|
| 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.
|
|
Commutative rings.
|
|
Commutative algebra.
|
|
Approximation theory.
|
|
Approximation theory
|
|
Commutative algebra
|
|
Commutative rings
|
|
Prüfer rings
|
| Form |
Electronic book
|
| Author |
Kaiser, Tobias, 1975-
|
| ISBN |
9783319032122 |
|
3319032127 |
|
