Manis valuations and Prüfer extensions II / Manfred Knebusch, Tobias Kaiser

• Autore: Knebusch, Manfred
• 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
• Serie: Lecture notes in mathematics, 0075-8434 ; 2103