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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the completeness of factor rings


Authors: S. Loepp and C. Rotthaus
Journal: Proc. Amer. Math. Soc. 130 (2002), 2189-2195
MSC (2000): Primary 13J05, 13J10
Published electronically: January 17, 2002
MathSciNet review: 1896398
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Abstract: Let $T$ be a complete local domain containing the integers with maximal ideal $M$ such that $\vert T/M\vert$ is at least the cardinality of the real numbers. Let $p$ be a nonmaximal prime ideal of $T$ such that $T_{p}$ is a regular local ring. We construct an excellent local ring $A$ such that the completion of $A$ is $T$, the generic formal fiber of $A$ is local with maximal ideal $p$ and if $I$ is a nonzero ideal of $A$, then $A/I$ is complete.


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Additional Information

S. Loepp
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: sloepp@williams.edu

C. Rotthaus
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: rotthaus@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06334-7
PII: S 0002-9939(02)06334-7
Keywords: Local rings, completions, factor rings, excellent rings
Received by editor(s): June 28, 2000
Received by editor(s) in revised form: February 22, 2001
Published electronically: January 17, 2002
Additional Notes: The first author appreciates the hospitality of Michigan State University, where this project was conducted, and is grateful for the support of the National Science Foundation via DMS #9973069
The second author thanks the National Science Foundation for their support via DMS #980122
Communicated by: Wolmer V. Vasconselos
Article copyright: © Copyright 2002 American Mathematical Society