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Titlebook: Manis Valuations and Prüfer Extensions II; Manfred Knebusch,Tobias Kaiser Book 2014 The Editor(s) (if applicable) and The Author(s), under

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發(fā)表于 2025-3-21 20:09:31 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Manis Valuations and Prüfer Extensions II
編輯Manfred Knebusch,Tobias Kaiser
視頻videohttp://file.papertrans.cn/624/623429/623429.mp4
概述Includes supplementary material:
叢書名稱Lecture Notes in Mathematics
圖書封面Titlebook: Manis Valuations and Prüfer Extensions II;  Manfred Knebusch,Tobias Kaiser Book 2014 The Editor(s) (if applicable) and The Author(s), under
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 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..
出版日期Book 2014
關(guān)鍵詞Approximation theorems; Kronecker extensions; Manis valuations and Prüfer extensions; Multiplicative id
版次1
doihttps://doi.org/10.1007/978-3-319-03212-2
isbn_softcover978-3-319-03211-5
isbn_ebook978-3-319-03212-2Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Manfred Knebusch,Tobias Kaiserematics is required. More than 700 exercises are included and they form an integral part of the material. Many exercises are in reality supplemental material and their solutions are included.978-1-4471-7134-8978-1-4471-6407-4Series ISSN 1610-3947 Series E-ISSN 2197-8441
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Book 2014Another 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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0075-8434 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..978-3-319-03211-5978-3-319-03212-2Series ISSN 0075-8434 Series E-ISSN 1617-9692
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發(fā)表于 2025-3-23 07:31:14 | 只看該作者
Manfred Knebusch,Tobias Kaisercations ranging from association rules, clustering algorithmData mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph
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