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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

One-dimensional bad Noetherian domains


Author: Bruce Olberding
Journal: Trans. Amer. Math. Soc. 366 (2014), 4067-4095
MSC (2010): Primary 13E05, 13B35, 13B22; Secondary 13F40
Published electronically: February 26, 2014
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05921-7
PII: S 0002-9947(2014)05921-7
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.