Manis Valuations and Prüfer Extensions II [[electronic resource] /] / by Manfred Knebusch, Tobias Kaiser
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| Autore: |
Knebusch Manfred
|
| Titolo: |
Manis Valuations and Prüfer Extensions II [[electronic resource] /] / by Manfred Knebusch, Tobias Kaiser
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
| Edizione: | 1st ed. 2014. |
| Descrizione fisica: | 1 online resource (XII, 190 p.) |
| Disciplina: | 512.44 |
| Soggetto topico: | Commutative algebra |
| Commutative rings | |
| Commutative Rings and Algebras | |
| Classificazione: | 13A1813A1513F0513F3013B3011J61 |
| Persona (resp. second.): | KaiserTobias |
| Note generali: | Bibliographic Level Mode of Issuance: Monograph |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Manis Valuations and Prüfer Extensions II |
| ISBN: | 3-319-03212-7 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 996203276603316 |
| Lo trovi qui: | Univ. di Salerno |
| Opac: | Controlla la disponibilità qui |
Serie:
Lecture Notes in Mathematics, . 0075-8434 ; ; 2103