LEADER 02616nam a2200373 i 4500 001 991002951599707536 006 m o d 007 cr ||| 008 160722s2014 sz ob 001 0 eng d 020 $a9783319032122 024 7 $a10.1007/978-3-319-03212-2$2doi 035 $ab14259187-39ule_inst 082 0 $a512.44$223 084 $aAMS 13A18 084 $aAMS 13B02 084 $aAMS 13F05 084 $aLC QA251.3 100 1 $aKnebusch, Manfred$054845 245 10$aManis valuations and Prüfer extensions II$h[e-book] /$cManfred Knebusch, Tobias Kaiser 260 $aCham :$bSpringer,$c2014 300 $a1 online resource (xii, 190 p.) 440 0$aLecture notes in mathematics,$x1617-9692 ;$v2103 505 0 $aOverrings 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 520 $aThis volume is a sequel to 'Manis Valuation and Prüfer Extensions I,' LNM1791. The Prüfer extensions of a commutative ring A are roughly those commutative ring extensions R / A,where commutative algebra is governed by Manis valuations on R with integral values on A. These valuations then turn out to belong to the particularly amenable subclass of PM (=Prüfer-Manis) valuations. While in Volume I Prüfer extensions in general and individual PM valuations were studied, now the focus is on families of PM valuations. One highlight is the presentation of a very general and deep approximation theorem for PM valuations, going back to Joachim Gräter's work in 1980, a far-reaching extension of the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called 'Kronecker extensions,' where PM valuations are put to use in arbitrary commutative ring extensions in a way that ultimately goes back to the work of Leopold Kronecker 650 0$aAlgebra 700 1 $aKaiser, Tobias$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0524807 773 0 $aSpringer eBooks 776 08$aPrinted edition:$z9783319032115 856 40$uhttp://link.springer.com/book/10.1007%2F978-3-319-03212-2$zAn electronic book accessible through the World Wide Web 907 $a.b14259187$b03-03-22$c22-07-16 912 $a991002951599707536 996 $aManis valuations and Prüfer extensions II$9820720 997 $aUNISALENTO 998 $ale013$b22-07-16$cm$d@ $e-$feng$gsz $h0$i0