Description

Book Synopsis
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.

Table of Contents
  • Introduction
  • Tools
  • More tools
  • First examples of the construction
  • The Inclusion Construction
  • Flatness and the Noetherian property
  • The flat locus of an extension of polynomial rings
  • Excellent rings and formal fibers
  • Height-one prime ideals and weak flatness
  • Insider Construction details
  • Integral closure under extension to the completion
  • Iterative examples
  • Approximating discrete valuation rings by regular local rings
  • Non-Noetherian examples of dimension 3
  • Noetherian properties of non-Noetherian rings
  • Non-Noetherian examples in higher dimension
  • The Homomorphic Image Construction
  • Catenary local rings with geometrically normal fibers
  • An Ogoma-like example
  • Multi-ideal-adic completions of Noetherian rings
  • Noetherian flatness and multi-adic constructions
  • Idealwise algebraic independence
  • Idealwise algebraic independence II
  • Krull domains with Noetherian $x$-adic completions
  • Inclusion Constructions over excellent normal local domains
  • Wierstrass techniques for generic fiber rings
  • Generic fiber rings of mixed polynomial-power series rings
  • Mixed polynomial-power series rings and relations among their spectra
  • Extensions of local domains with trivial generic fiber
  • Constructions and examples discussed in this book
  • Bibliography
  • Index

Integral Domains Inside Noetherian Power Series

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    A Paperback by William Heinzer, Christel Rotthaus, Sylvia Wiegand

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 8/30/2022 12:00:00 AM
      ISBN13: 9781470466428, 978-1470466428
      ISBN10: 1470466422

      Description

      Book Synopsis
      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.

      Table of Contents
      • Introduction
      • Tools
      • More tools
      • First examples of the construction
      • The Inclusion Construction
      • Flatness and the Noetherian property
      • The flat locus of an extension of polynomial rings
      • Excellent rings and formal fibers
      • Height-one prime ideals and weak flatness
      • Insider Construction details
      • Integral closure under extension to the completion
      • Iterative examples
      • Approximating discrete valuation rings by regular local rings
      • Non-Noetherian examples of dimension 3
      • Noetherian properties of non-Noetherian rings
      • Non-Noetherian examples in higher dimension
      • The Homomorphic Image Construction
      • Catenary local rings with geometrically normal fibers
      • An Ogoma-like example
      • Multi-ideal-adic completions of Noetherian rings
      • Noetherian flatness and multi-adic constructions
      • Idealwise algebraic independence
      • Idealwise algebraic independence II
      • Krull domains with Noetherian $x$-adic completions
      • Inclusion Constructions over excellent normal local domains
      • Wierstrass techniques for generic fiber rings
      • Generic fiber rings of mixed polynomial-power series rings
      • Mixed polynomial-power series rings and relations among their spectra
      • Extensions of local domains with trivial generic fiber
      • Constructions and examples discussed in this book
      • Bibliography
      • Index

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