TY - BOOK ID - 699656 TI - Manis Valuations and Prüfer Extensions II AU - Knebusch, Manfred. AU - Kaiser, Tobias. PY - 2014 SN - 3319032127 3319032119 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Commutative algebra. KW - Commutative rings. KW - Prüfer rings. KW - Commutative semihereditary domains KW - Commutative semihereditary entire rings KW - Domains, Commutative semihereditary KW - Domains, Prüfer KW - Entire rings, Commutative semihereditary KW - Prüfer domains KW - Prüfer's domains KW - Prüfer's rings KW - Semihereditary domains, Commutative KW - Semihereditary entire rings, Commutative KW - Rings (Algebra) KW - Algebra KW - Algebra. KW - Commutative Rings and Algebras. KW - Mathematics KW - Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:699656 AB - 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. ER -