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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.

Commutative algebra. --- Commutative rings. --- Prüfer rings. --- Commutative semihereditary domains --- Commutative semihereditary entire rings --- Domains, Commutative semihereditary --- Domains, Prüfer --- Entire rings, Commutative semihereditary --- Prüfer domains --- Prüfer's domains --- Prüfer's rings --- Semihereditary domains, Commutative --- Semihereditary entire rings, Commutative --- Rings (Algebra) --- Algebra --- Algebra. --- Commutative Rings and Algebras. --- Mathematics --- Mathematical analysis

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378.4 <43 JENA> --- 378.4 <43 JENA> Universiteiten--Duitsland voor 1945 en na 1989--JENA --- Universiteiten--Duitsland voor 1945 en na 1989--JENA --- Education and state --- Socialism and education --- Universities and colleges --- Colleges --- Degree-granting institutions --- Higher education institutions --- Higher education providers --- Institutions of higher education --- Postsecondary institutions --- Public institutions --- Schools --- Education, Higher --- Education and socialism --- Education --- History --- Friedrich-Schiller-Universität Jena --- Ĭenskiĭ gosudarstvennyĭ universitet --- Jena. --- Fr. Šileris saxelobis Ienis universiteti --- Ĭenskiĭ universitet im. F. Shillera --- Schiller-Universität Jena --- Germany (East). --- Jena University --- Ĭenskiĭ gosudarstvennyĭ universitet im. Fridrikha Shillera --- FSU Jena --- Friedrich-Schiller-Universität (Jena, Germany) --- University of Jena --- Universität Jena --- Friedrich Schiller University --- Friedrich-Schiller University of Jena --- FSU (Friedrich-Schiller-Universität) --- Uni Jena

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Friedrich-Schiller-Universität Jena --- Universität Jena --- Universität Jena --- History --- History --- History