TY - BOOK
AU - Knebusch, Manfred.
AU - Kaiser, Tobias.
ED - SpringerLink (Online service)
TI - Manis Valuations and Prüfer Extensions II
T2 - Lecture Notes in Mathematics,
SN - 9783319032
AV - QA251.3
U1 - 512.44 23
PY - 2014///
CY - Cham
PB - Springer International Publishing, Imprint: Springer
KW - Mathematics
KW - Algebra
KW - Commutative Rings and Algebras
N1 - 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
N2 - This volume is a sequel to â€œManis Valuation and PrÃ¼fer Extensions I,â€ LNM1791. The PrÃ¼fer 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 (=PrÃ¼fer-Manis) valuations. While in Volume I PrÃ¼fer 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 GrÃ¤terâ€™s work in 1980, a far-reaching extension of the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called â€œKronecker extensions,â€ where PM valuations are put to use in Â arbitrary commutative Â ring extensions in a way that ultimately goes back to the work of Leopold Kronecker
UR - http://dx.doi.org/10.1007/978-3-319-03212-2
ER -