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|a Knebusch, Manfred.
|e author.
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|4 http://id.loc.gov/vocabulary/relators/aut
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|a Manis Valuations and Prüfer Extensions II
|h [electronic resource] /
|c by Manfred Knebusch, Tobias Kaiser.
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|a 1st ed. 2014.
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| 264 |
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|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2014.
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|a XII, 190 p.
|b online resource.
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 2103
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|a Springer eBook Collection
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|a 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.
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|a 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.
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|a Loaded electronically.
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|a Electronic access restricted to members of the Holy Cross Community.
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|a Commutative algebra.
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|a Commutative rings.
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