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

DOI:
https://doi.org/10.1090/S0002-9939-02-06334-7

Published electronically:
January 17, 2002

MathSciNet review:
1896398

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a complete local domain containing the integers with maximal ideal such that is at least the cardinality of the real numbers. Let be a nonmaximal prime ideal of such that is a regular local ring. We construct an excellent local ring such that the completion of is , the generic formal fiber of is local with maximal ideal and if is a nonzero ideal of , then 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:
https://doi.org/10.1090/S0002-9939-02-06334-7

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