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Two counterexamples in normalization
Author(s):
Shreeram
S.
Abhyankar;
Ben
Kravitz
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3521-3523.
MSC (2000):
Primary 14A05
Posted:
July 27, 2007
MathSciNet review:
2336566
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Abstract:
In this paper, we offer a correction to Commutative Algebra by Oscar Zariski and Pierre Samuel by noting two erroneous theorems and offering counterexamples for each.
References:
-
- 1.
- S. S. Abhyankar, Lectures on Algebra, Volume I, World Scientific, Hackensack, NJ, 2006.
- 2.
- R. C. Heitmann, Characterization of Completions of Unique Factorization Domains, Trans. Amer. Math. Soc., vol. 337, no. 1, Amer. Math. Soc. (May, 1993), Providence, RI, pp. 379-387. MR 1102888 (93g:13006)
- 3.
- M. Nagata, Local Rings, Interscience Publishers, New York, 1962. MR 0155856 (27:5790)
- 4.
- D. Rees, A Note on Analytically Unramified Local Rings, Journal London Math. Soc., vol. 36, London Math. Soc. (1961), pp. 24-28. MR 0126465 (23:A3761)
- 5.
- O. Zariski and P. Samuel, Commutative Algebra, Volume I, Springer-Verlag, New York, 1960.
- 6.
- O. Zariski and P. Samuel, Commutative Algebra, Volume II, Springer-Verlag, New York, 1960. MR 0120249 (22:11006)
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Additional Information:
Shreeram
S.
Abhyankar
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
ram@cs.purdue.edu
Ben
Kravitz
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
bkravitz@math.purdue.edu
DOI:
10.1090/S0002-9939-07-09010-7
PII:
S 0002-9939(07)09010-7
Keywords:
Commutative algebra
Received by editor(s):
August 28, 2006
Posted:
July 27, 2007
Additional Notes:
The first author's work was partly supported by NSF Grant DMS 99-88166 and NSA Grant MSP H98230-05-1-0040.
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2007,
American Mathematical Society
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