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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
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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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