A remark concerning multiplicities

Huneke, Craig

doi:10.1090/S0002-9939-1982-0656095-2

A remark concerning multiplicities
HTML articles powered by AMS MathViewer

by Craig Huneke

Proc. Amer. Math. Soc. 85 (1982), 331-332

DOI: https://doi.org/10.1090/S0002-9939-1982-0656095-2

PDF | Request permission

Abstract:

We prove that if a complete local ring $A$ containing a field satisfies Serre’s condition ${S_n}$ and the multiplicity of $A$ is at most $n$, then $A$ must be Cohen-Macaulay.

References

Maurice Auslander and Mark Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, R.I., 1969. MR 0269685
E. Graham Evans and Phillip Griffith, The syzygy problem, Ann. of Math. (2) 114 (1981), no. 2, 323–333. MR 632842, DOI 10.2307/1971296
M. Hochster, Contracted ideals from integral extensions of regular rings, Nagoya Math. J. 51 (1973), 25–43. MR 349656
Masayoshi Nagata, Local rings, Robert E. Krieger Publishing Co., Huntington, N.Y., 1975. Corrected reprint. MR 0460307
D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145–158. MR 59889, DOI 10.1017/s0305004100029194
Jean-Pierre Serre, Valeurs propres des endomorphismes de Frobenius (d’après P. Deligne), Séminaire Bourbaki, 26ème année (1973/1974), Lecture Notes in Math., Vol. 431, Springer, Berlin, 1975, pp. Exp. No. 446, pp. 190–204 (French). MR 0463177