Erschienen: 31.07.2010 Abbildung von Schoutens | The Use of Ultraproducts in Commutative Algebra | 1st Edition. | 2010 | 1999


The Use of Ultraproducts in Commutative Algebra

1st Edition. 2010. Buch. x, 210 S. Bibliographien. Softcover

Springer. ISBN 978-3-642-13367-1

Format (B x L): 15,5 x 23,5 cm

Gewicht: 700 g

In englischer Sprache

Das Werk ist Teil der Reihe: Lecture Notes in Mathematics; 1999


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.


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