The Use of Ultraproducts in Commutative Algebra (Lecture Notes in Mathematics, Band 1999) - Softcover

Schoutens, Hans

 
9783642133671: The Use of Ultraproducts in Commutative Algebra (Lecture Notes in Mathematics, Band 1999)
Softcover
ISBN 10: 3642133673 ISBN 13: 9783642133671
Verlag: Springer, 2010

Inhaltsangabe

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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Von der hinteren Coverseite

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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Verlag
Springer
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
3642133673
ISBN 13 
9783642133671
Einband
Taschenbuch
Anzahl der Seiten
220
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Weitere beliebte Ausgaben desselben Titels

9783642133695: The Use of Ultraproducts in Commutative Algebra

Vorgestellte Ausgabe

ISBN 10:  364213369X ISBN 13:  9783642133695
Verlag: Springer, 2010
Softcover