Vai al contenuto principale della pagina
Autore: | Knebusch, Manfred |
Titolo: | Manis valuations and Prüfer extensions II / Manfred Knebusch, Tobias Kaiser |
Pubblicazione: | Cham : Springer, 2014 |
Descrizione fisica: | xii, 190 p. : ill. ; 24 cm |
Disciplina: | 512.44 |
Soggetto topico: | Algebra |
Classificazione: | AMS 13A18 |
AMS 13B02 | |
AMS 13F05 | |
LC QA251.3 | |
Altri autori: | Kaiser, Tobiasauthor |
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 |
ISBN: | 9783319032115 |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 991002951659707536 |
Lo trovi qui: | Univ. del Salento |
Opac: | Controlla la disponibilità qui |