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Record Nr. |
UNISALENTO991002951659707536 |
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Autore |
Knebusch, Manfred |
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Titolo |
Manis valuations and Prüfer extensions II / Manfred Knebusch, Tobias Kaiser |
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Pubbl/distr/stampa |
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ISBN |
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Descrizione fisica |
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xii, 190 p. : ill. ; 24 cm |
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Collana |
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Lecture notes in mathematics, 0075-8434 ; 2103 |
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Classificazione |
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AMS 13A18 |
AMS 13B02 |
AMS 13F05 |
LC QA251.3 |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Overrings 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 |
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Sommario/riassunto |
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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 |
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