Integral Domains Inside Noetherian Power Series Rings

ISBN-13: 9781470466428 / Miękka / 2021 / 426 str.

Sylvia Wiegand

Spis treści

• 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