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OverviewPower 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. Full Product DetailsAuthor: William Heinzer , Christel Rotthaus , Sylvia WiegandPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.672kg ISBN: 9781470466428ISBN 10: 1470466422 Pages: 426 Publication Date: 30 August 2022 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction 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 IndexReviewsAuthor InformationWilliam Heinzer, Purdue University, West Lafayette, IN. Christel Rotthaus, Michigan State University, East Lansing, MI. Sylvia Wiegand, University of Nebraska, Lincoln, NE. Tab Content 6Author Website:Countries AvailableAll regions |
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