Integral domains inside Noetherian power series rings : constructions and examples

著者

• Heinzer, William J
• Rotthaus, Christel
• Wiegand, Sylvia

書誌事項

Integral domains inside Noetherian power series rings : constructions and examples

William Heinzer, Christel Rotthaus, Sylvia Wiegand

（Mathematical surveys and monographs, v. 259）

American Mathematical Society, c2021

• : pbk

タイトル別名

Constructions inside power series rings

注記

Includes bibliographical references (p. 407-415) and index

内容説明・目次

内容説明

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.

目次

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

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BC10659898
• ISBN:
  • 9781470466428
• LCCN: 2021021513
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xi, 426 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA251.3
  • DC23 : 512/.44
  • DC23 : 512.44
• 件名:
  • LCSH : Noetherian rings
  • LCSH : Integral domains
• 親書誌ID:
  • BA00134419