Integral Domains Inside Noetherian Power Series Rings
Constructions and Examples
William Heinzer (Author), Christel Rotthaus (Author), Sylvia Wiegand (Author)
9781470466428
Paperback / softback, published 30 August 2022
426 pages 25.4 x 17.8 x 2 cm, 0.672 kg
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.
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
