| 书目名称 | Manis Valuations and Prüfer Extensions II |
| 编辑 | Manfred Knebusch,Tobias Kaiser |
| 视频video | |
| 概述 | Includes supplementary material: |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | .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.. |
| 出版日期 | Book 2014 |
| 关键词 | Approximation theorems; Kronecker extensions; Manis valuations and Prüfer extensions; Multiplicative id |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-03212-2 |
| isbn_softcover | 978-3-319-03211-5 |
| isbn_ebook | 978-3-319-03212-2Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 20:09:31
