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The Use of Ultraproducts in Commutative Algebra by Hans Schoutens
The Use of Ultraproducts in Commutative Algebra by Hans Schoutens
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The Use of Ultraproducts in Commutative Algebra

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Description

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.
Release date Australia
July 31st, 2010
Audience
  • Professional & Vocational
Illustrations
X, 210 p.
Pages
210
Dimensions
156x234x11
ISBN-13
9783642133671
Product ID
7888278

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