Lecture Notes in Mathematics

Manis Valuations and Prüfer Extensions II

Authors: Knebusch, Manfred, Kaiser, Tobias

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About this book

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.

Table of contents (3 chapters)

  • Overrings and PM-Spectra

    Knebusch, Manfred (et al.)

    Pages 1-57

  • Approximation Theorems

    Knebusch, Manfred (et al.)

    Pages 59-121

  • Kronecker Extensions and Star Operations

    Knebusch, Manfred (et al.)

    Pages 123-178

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-03212-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-03211-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Manis Valuations and Prüfer Extensions II
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2103
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-03212-2
DOI
10.1007/978-3-319-03212-2
Softcover ISBN
978-3-319-03211-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 190
Topics