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Book synopsis

This volume is a sequel of 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 well amenable subclass of PM (=Prüfer-Manis) valuations. While in Volume I Prüfer extensions in general and individual PM-valuations have been studied, now the stress 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 1980, a far reaching extension of the classical weak approximation theorem in arithmetics. 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, which ultimately goes back to Leopold Kronecker.§Prüfer extensions seem to be mandatory to understand certain aspects of real and p-adic geometry.

Book details

Book category Books in English Mathematics & science Mathematics Algebra

• Full title: Manis Valuations and Prufer Extensions II
• Author: Tobias Kaiser, Manfred Knebusch
• Language: English
• Binding: Paperback
• Number of pages: 190
• EAN: 9783319032115
• ISBN: 3319032119
• ID: 02172089
• Publisher: Springer International Publishing AG
• Weight: 3168 g
• Dimensions: 235 × 155 × 12 mm
• Date of publishing: 21. March 2014

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