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A characterization of Gorenstein rings in characteristic
Author(s):
S.
P.
Dutta
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1637-1643.
MSC (1991):
Primary 13D02, 13H10
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Abstract:
A new characterization of Gorenstein rings in characteristic is proved. It involves asymptotic behaviour of lengths of modules under the Frobenius map.
References:
- [D1]
- S. P. Dutta, Frobenius and Multiplicities, J. Algebra No. 2 85 (1983), 424-448. MR 85f:13022
- [D2]
- S. P. Dutta,
and Frobenius, J. Algebra No. 1 127 (1989), 163-177. MR 91g:13018 - [K]
- I. Kaplansky, Commutative Rings, Revised Edition, Univ. of Chicago Press (1974). MR 49:10674
- [L]
- S. Lichtenbaum, On the vanishing of
in regular local rings, Illinois J. Math. 10 (1966), 220-226. MR 32:5688 - [P-S]
- C. Peskine and L. Szpiro, Dimension projective finie et cohomologie local, Publ. I.H.E.S. Paris 42 (1973),
47-119. MR 51:10330 - [R]
- P. Roberts, Intersection theorems, Commutative algebra, Hochster, Huneke, Sally Editors, MSRI Publications, 15, Springer-Verlag (1989), 417-437. MR 90j:13024
- [S]
- G. Seibert, Complexes with homology of finite length and Frobenius functions, J. Algebra 125 (1989), 278-287. MR 90j:13012
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Additional Information:
S.
P.
Dutta
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email:
dutta@math.uiuc.edu
DOI:
10.1090/S0002-9939-98-04228-2
PII:
S 0002-9939(98)04228-2
Received by editor(s):
March 15, 1996
Received by editor(s) in revised form:
November 26, 1996
Additional Notes:
This research was partially supported by an NSF grant and an NSA grant.
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
1998,
American Mathematical Society
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