Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-01-06113-5
Published electronically: August 29, 2001
MathSciNet review: 1866016
Full-text PDF

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 [Enhancements On Off] (What's this?)

  • [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: https://doi.org/10.1090/S0002-9939-01-06113-5
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

American Mathematical Society