Manis valuations and Prüfer extensions II

書誌事項

Manis valuations and Prüfer extensions II

Manfred Knebusch, Tobias Kaiser

(Lecture notes in mathematics, 2103)

Springer, c2014

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注記

Includes bibliographical references (p. 181-182) and indexes

内容説明・目次

内容説明

This volume is a sequel to "Manis Valuation and Prufer Extensions I," LNM1791. The Prufer 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 (=Prufer-Manis) valuations. While in Volume I Prufer 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 Grater'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.

目次

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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詳細情報
  • NII書誌ID(NCID)
    BB15296808
  • ISBN
    • 9783319032115
  • LCCN
    2014930747
  • 出版国コード
    sz
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cham
  • ページ数/冊数
    xii, 190 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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