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＜電子ブック＞
Manis Valuations and Prüfer Extensions II / by Manfred Knebusch, Tobias Kaiser
(Lecture Notes in Mathematics. ISSN:16179692 ; 2103)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
大きさ	XII, 190 p : online resource
著者標目	*Knebusch, Manfred author Kaiser, Tobias author SpringerLink (Online service)
件　名	LCSH:Commutative algebra LCSH:Commutative rings FREE:Commutative Rings and Algebras
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-03212-2

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