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The Use of Ultraproducts in Commutative Algebra

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 ultraprodu...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Schoutens, Hans (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2010.
Edición:1st ed. 2010.
Colección:Lecture Notes in Mathematics, 1999
Temas:
Acceso en línea:Texto Completo
Descripción
Sumario: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.
Descripción Física:X, 210 p. online resource.
ISBN:9783642133688
ISSN:1617-9692 ;