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Catalogue Information
Field name	Details
Dewey Class	512.44
Title	Manis Valuations and Prüfer Extensions II ([Ebook]) / by Manfred Knebusch, Tobias Kaiser.
Author	Knebusch, Manfred
Added Personal Name	Kaiser, Tobias
Other name(s)	SpringerLink (Online service)
Publication	Cham : Springer International Publishing, 2014.
Physical Details	XII, 190 pages : online resource.
ISBN	9783319032122
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-03212-2
Links to Related Works	Subject References: Algebra . Commutative Rings and Algebras . Mathematics . Authors: author . Kaiser, Tobias . Knebusch, Manfred . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512.44 . 512.44 (DDC 23) .

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Manis Valuations and Prüfer Extensions II

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