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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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One-dimensional bad Noetherian domains
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by Bruce Olberding PDF
Trans. Amer. Math. Soc. 366 (2014), 4067-4095 Request permission

Abstract:

Local Noetherian domains arising as local rings of points of varieties or in the context of algebraic number theory are analytically unramified, meaning their completion has no nontrivial nilpotent elements. However, looking elsewhere, many sources of analytically ramified local Noetherian domains have been exhibited over the last seventy-five years. We give a unified approach to a number of such examples by describing classes of DVRs which occur as the normalization of an analytically ramified local Noetherian domain, as well as some that do not occur as such a normalization. We parameterize these examples, or at least large classes of them, using the module of Kähler differentials of a relevant field extension.
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Additional Information
  • Bruce Olberding
  • Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001
  • MR Author ID: 333074
  • Received by editor(s): April 18, 2011
  • Received by editor(s) in revised form: February 6, 2012, and July 15, 2012
  • Published electronically: February 26, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 4067-4095
  • MSC (2010): Primary 13E05, 13B35, 13B22; Secondary 13F40
  • DOI: https://doi.org/10.1090/S0002-9947-2014-05921-7
  • MathSciNet review: 3206452