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Non-Noetherian Commutative Ring Theory

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概要 Commutative Ring Theory emerged as a distinct field of research in math ematics only at the beginning of the twentieth century. It is rooted in nine teenth century major works in Number Theory and Alg...braic Geometry for which it provided a useful tool for proving results. From this humble origin, it flourished into a field of study in its own right of an astonishing richness and interest. Nowadays, one has to specialize in an area of this vast field in order to be able to master its wealth of results and come up with worthwhile contributions. One of the major areas of the field of Commutative Ring Theory is the study of non-Noetherian rings. The last ten years have seen a lively flurry of activity in this area, including: a large number of conferences and special sections at national and international meetings dedicated to presenting its results, an abundance of articles in scientific journals, and a substantial number of books capturing some of its topics. This rapid growth, and the occasion of the new Millennium, prompted us to embark on a project aimed at presenting an overview of the recent research in the area. With this in mind, we invited many of the most prominent researchers in Non-Noetherian Commutative Ring Theory to write expository articles representing the most recent topics of research in this area.続きを見る
目次 1 GCD Domains, Gauss' Lemma, and Contents of Polynomials
2 The Class Group and Local Class Group of an Integral Domain
3 Mori Domains
4 What's New About Integer-Valued Polynomials on a Subset?
5 Half-Factorial Domains, a Survey
6 On Generalized Lengths of Factorizations in Dedekind and Krull Domains
7 Recent Progress on Going-Down I
8 Localizing Systems and Semistar Operations
9 Ideal Theory in Pullbacks
10 Commutative Rings of Dimension 0
11 Finite Conductor Rings with Zero Divisors
12 Construction of Ideal Systems with Nice Noetherian Properties
13 Generalized Local Rings and Finite Generation of Powers of Ideals
14 Connecting Trace Properties
15 Constructing Examples of Integral Domains by Intersecting Valuation Domains
16 Examples Built With D+M, A+XB[X] and Other Pullback Constructions
17 T-Closedness
18 E-rings and Related Structures
19 Prime Ideals and Decompositions of Modules
20 Putting t-Invertibility to Use
21 One Hundred Problems in Commutative Ring Theory.
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登録日 2014.09.18
更新日 2017.11.26