Lecture Notes in Mathematics

The Use of Ultraproducts in Commutative Algebra

Authors: Schoutens, Hans

  • Presents a novel use of ultraproducts in algebra
  • Provides a gentle introduction to tight closure in characteristic zero
  • Includes a survey chapter on various flatness criteria
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About this book

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.

Table of contents (1 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-13368-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-13367-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Use of Ultraproducts in Commutative Algebra
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1999
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-13368-8
DOI
10.1007/978-3-642-13368-8
Softcover ISBN
978-3-642-13367-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 210
Topics