Manis Valuations and Prüfer Extensions II / by Manfred Knebusch, Tobias Kaiser.

Format:

Book

Author/Creator:

Knebusch, Manfred, author.

Kaiser, Tobias, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2103.

Lecture Notes in Mathematics, 0075-8434 ; 2103

Language:

English

Subjects (All):

Algebra.

Commutative Rings and Algebras.

Local Subjects:

Commutative Rings and Algebras.

Physical Description:

1 online resource (XII, 190 pages).

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2014.

System Details:

text file PDF

Summary:

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:

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

Appendix

References

Index.

Other Format:

Printed edition:

ISBN:

9783319032122

Access Restriction:

Restricted for use by site license.