Manis Valuations and Prüfer Extensions II [electronic resource] /Material type: BookSeries: Lecture Notes in Mathematics: 2103Publisher: Cham : Springer International Publishing : 2014.Description: XII, 190 p. online resource.ISBN: 9783319032122.Subject(s): Mathematics | Algebra | Mathematics | Commutative Rings and AlgebrasDDC classification: 512.44 Online resources: Click here to access online
Central Library, IISER Bhopal
OPAC URL: http://webopac.iiserb.ac.in/
|512.44 (Browse shelf)
|Not for loan
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.
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.