This volume is a sequel to "Manis Valuation and Pr�fer Extensions I," LNM1791. The Pr�fer 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 (=Pr�fer-Manis) valuations. While in Volume I Pr�fer extensions in general and individual PM valuations were studied, now the focus is on families of PM valuations. One ...
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This volume is a sequel to "Manis Valuation and Pr�fer Extensions I," LNM1791. The Pr�fer 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 (=Pr�fer-Manis) valuations. While in Volume I Pr�fer 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 Gr�ter'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.
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New. Trade paperback (US). Glued binding. 190 p. Lecture Notes in Mathematics, 2103. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
