By Manfred Knebusch, Tobias Kaiser
This quantity is a sequel to “Manis Valuation and Prüfer Extensions I,” LNM1791. The Prüfer extensions of a commutative ring A are approximately these commutative ring extensions R / A, the place commutative algebra is ruled through Manis valuations on R with indispensable values on A. those valuations then prove to belong to the fairly amenable subclass of PM (=Prüfer-Manis) valuations. whereas in quantity I Prüfer extensions more often than not and person PM valuations have been studied, now the focal point is on households of PM valuations. One spotlight is the presentation of a really common and deep approximation theorem for PM valuations, going again to Joachim Gräter’s paintings in 1980, a far-reaching extension of the classical vulnerable approximation theorem in mathematics. one other spotlight is a concept of so known as “Kronecker extensions,” the place PM valuations are placed to exploit in arbitrary commutative ring extensions in a manner that eventually is going again to the paintings of Leopold Kronecker.
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