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Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples
About this Title
William Heinzer, Purdue University, West Lafayette, IN, Christel Rotthaus, Michigan State University, East Lansing, MI and Sylvia Wiegand, University of Nebraska, Lincoln, NE
Publication: Mathematical Surveys and Monographs
Publication Year:
2021; Volume 259
ISBNs: 978-1-4704-6642-8 (print); 978-1-4704-6733-3 (online)
DOI: https://doi.org/10.1090/surv/259
Table of Contents
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Front/Back Matter
Chapters
- 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
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