Integral Domains Inside Noetherian Power Series Rings

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

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