The use of ultraproducts in commutative algebra / by Hans Schoutens
- 作者： Schoutens, Hans.
- 其他作者：
- 其他題名：
- Springer eBooks
- 出版： Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg 2010
- 叢書名： Lecture notes in mathematics ,1999
- 主題： Ultraproducts. , Commutative algebra. , Mathematics. , Commutative Rings and Algebras. , Algebraic Geometry.
- ISBN： 9783642133688 (electronic bk.) 、 9783642133671 (paper)
- URL：
電子書
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讀者標籤：
- 系統號： 005173122 | 機讀編目格式
館藏資訊
In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.