Integral Domains Inside Noetherian Power Series Rings

Constructions and Examples

Häftad, Engelska, 2022

Av William Heinzer, Christel Rotthaus, Sylvia Wiegand

1 829 kr

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Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.

Produktinformation

Utgivningsdatum2022-08-30
Mått178 x 254 x undefined mm
Vikt672 g
FormatHäftad
SpråkEngelska
SerieMathematical Surveys and Monographs
Antal sidor426
FörlagAmerican Mathematical Society
ISBN9781470466428

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Algebra inom Naturvetenskap och teknik

IntroductionToolsMore toolsFirst examples of the constructionThe Inclusion ConstructionFlatness and the Noetherian propertyThe flat locus of an extension of polynomial ringsExcellent rings and formal fibersHeight-one prime ideals and weak flatnessInsider Construction detailsIntegral closure under extension to the completionIterative examplesApproximating discrete valuation rings by regular local ringsNon-Noetherian examples of dimension 3Noetherian properties of non-Noetherian ringsNon-Noetherian examples in higher dimensionThe Homomorphic Image ConstructionCatenary local rings with geometrically normal fibersAn Ogoma-like exampleMulti-ideal-adic completions of Noetherian ringsNoetherian flatness and multi-adic constructionsIdealwise algebraic independenceIdealwise algebraic independence IIKrull domains with Noetherian $x$-adic completionsInclusion Constructions over excellent normal local domainsWierstrass techniques for generic fiber ringsGeneric fiber rings of mixed polynomial-power series ringsMixed polynomial-power series rings and relations among their spectraExtensions of local domains with trivial generic fiberConstructions and examples discussed in this bookBibliographyIndex