LEADER 02456nam a2200325 i 4500 001 991002951659707536 008 160722s2014 sz b 001 0 eng d 020 $a9783319032115 024 7 $a10.1007/978-3-319-03212-2$2doi 035 $ab14259199-39ule_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 /$cManfred Knebusch, Tobias Kaiser 260 $aCham :$bSpringer,$c2014 300 $axii, 190 p. :$bill. ;$c24 cm 440 0$aLecture notes in mathematics,$x0075-8434 ;$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 907 $a.b14259199$b11-11-16$c22-07-16 912 $a991002951659707536 945 $aLE013 13A KNE11 (2014)$g1$i2013000293455$lle013$op$pE36.39$q-$rl$s- $t0$u1$v0$w1$x0$y.i15787011$z11-11-16 996 $aManis valuations and Prüfer extensions II$9820720 997 $aUNISALENTO 998 $ale013$b22-07-16$cm$da $e-$feng$gsz $h0$i0