Integral Domains Inside Noetherian Power Series Rings

Constructions and Examples

AvWilliam Heinzer,Christel Rotthaus

Häftad, Engelska, 2022

Del i serien Mathematical Surveys and Monographs

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Beskrivning

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

Utgivningsdatum:2022-08-30
Mått:178 x 254 x undefined mm
Vikt:672 g
Format:Häftad
Språk:Engelska
Serie:Mathematical Surveys and Monographs
Antal sidor:426
Förlag:American Mathematical Society
ISBN:9781470466428

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

William Heinzer, Purdue University, West Lafayette, IN.Christel Rotthaus, Michigan State University, East Lansing, MI.Sylvia Wiegand, University of Nebraska, Lincoln, NE.

Innehållsförteckning

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