Manis Valuations and Prüfer Extensions II [electronic resource] / by Manfred Knebusch, Tobias Kaiser.
Knebusch, Manfred. author.
Kaiser, Tobias. author.
SpringerLink (Online service)
Mathematics.
Algebra.
QA251.3
512.44 23
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.
2014
Text
XII, 190 p.
http://dx.doi.org/10.1007/978-3-319-03212-2
eng
Springer eBooks
Lecture Notes in Mathematics, 0075-8434 ; 2103
Lecture Notes in Mathematics, 0075-8434 ; 2103