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A characterization of Gorenstein rings
in characteristic $\lowercase{p}\ (> 0)$


Author: S. P. Dutta
Journal: Proc. Amer. Math. Soc. 126 (1998), 1637-1643
MSC (1991): Primary 13D02, 13H10
DOI: https://doi.org/10.1090/S0002-9939-98-04228-2
MathSciNet review: 1443824
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Abstract | References | Similar Articles | Additional Information

Abstract: A new characterization of Gorenstein rings in characteristic $p\ (>0)$ is proved. It involves asymptotic behaviour of lengths of modules under the Frobenius map.


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

  • [D1] S. P. Dutta, Frobenius and Multiplicities, J. Algebra No. 2 85 (1983), 424-448. MR 85f:13022
  • [D2] S. P. Dutta, $\operatorname {Ext}$ 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 $\operatorname {Tor}$ 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: https://doi.org/10.1090/S0002-9939-98-04228-2
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
Article copyright: © Copyright 1998 American Mathematical Society

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