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.
Product Identifiers
Publisher
Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
ISBN-13
9783642133671
eBay Product ID (ePID)
96286454
Product Key Features
Author
Hans Schoutens
Publication Name
The Use of Ultra Products in Commutative Algebra
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2010
Type
Textbook
Number of Pages
210 Pages
Dimensions
Item Height
235mm
Item Width
155mm
Volume
1999
Item Weight
700g
Additional Product Features
Title_Author
Hans Schoutens
Series Title
Lecture Notes in Mathematics
Country/Region of Manufacture
Germany
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