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

 

Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular


Authors: Craig Huneke and Yongwei Yao
Journal: Proc. Amer. Math. Soc. 130 (2002), 661-665
MSC (1991): Primary 13D40, 13A30, 13H10
Published electronically: August 29, 2001
MathSciNet review: 1866016
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Abstract: We give a new and simple proof that unmixed local rings having Hilbert-Kunz multiplicity equal to $1$ must be regular.


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Additional Information

Craig Huneke
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: huneke@math.ukans.edu

Yongwei Yao
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: yyao@math.ukans.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06113-5
PII: S 0002-9939(01)06113-5
Keywords: Hilbert-Kunz, multiplicity, regular
Received by editor(s): June 5, 2000
Received by editor(s) in revised form: September 18, 2000
Published electronically: August 29, 2001
Additional Notes: The first author was partially supported by the NSF
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society