Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular

Author(s): Craig Huneke; Yongwei Yao
Journal: Proc. Amer. Math. Soc. 130 (2002), 661-665.
MSC (1991): Primary 13D40, 13A30, 13H10
Posted: August 29, 2001
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We give a new and simple proof that unmixed local rings having Hilbert-Kunz multiplicity equal to $1$ must be regular.

References:

[BH]
W. Bruns and J. Herzog, Cohen-Macaulay Rings, vol. 39, Cambridge studies in advanced mathematics, 1993. MR 95h:13020

[Ha]
D. Hanes, Special conditions on maximal Cohen-Macaulay modules, and applications to the theory of multiplicities, Thesis, University of Michigan, 1999.

[Ku1]
E. Kunz, On Noetherian rings of characteristic $p$, Amer. J. Math. 98 (1976), 999-1013. MR 55:5612

[Ku2]
E. Kunz, Characterizations of regular local rings of characteristic $p$, Amer. J. Math. 91 (1969), 772-784. MR 40:5609

[Mo]
P. Monsky, The Hilbert-Kunz function, Math. Annalen 263 (1983), 43-49. MR 84k:13012

[Na]
M. Nagata, Local Rings, Robert E. Kreiger Publishing Co., 1975. MR 57:301

[Sa]
P. Samuel, La notion de multiplicité en algébre et en géométrie algèbrique, I & II, J. Math. Pures. Appl. 30 (1951), 159-274. MR 13:980c; MR 13:980d

[WY]
K. Watanabe, K. Yoshida, Hilbert-Kunz multiplicity and an inequality between multiplicity and colength, J. Algebra 230 (2000), 295-317. CMP 2000:16

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13D40, 13A30, 13H10

Retrieve articles in all Journals with MSC (1991): 13D40, 13A30, 13H10

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: 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
Posted: August 29, 2001
Additional Notes: The first author was partially supported by the NSF
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 2001, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google