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The existence of finitely generated modules of finite Gorenstein injective dimension
Author(s):
Ryo
Takahashi
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3115-3121.
MSC (2000):
Primary 13D05;
Secondary 13H10
Posted:
May 12, 2006
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Abstract:
In this note, we study commutative Noetherian local rings having finitely generated modules of finite Gorenstein injective dimension. In particular, we consider whether such rings are Cohen-Macaulay.
References:
-
- 1.
- M. Anneaux, de Gorenstein, et torsion en algèbre commutative, Séminaire d'Algèbre Commutative dirigé par Pierre Samuel, 1966/67. Texte rédigé, d'après des exposés de Maurice Auslander, Marquerite Mangeney, Christian Peskine et Lucien Szpiro. École Normale Supérieure de Jeunes Filles, Secrétariat mathématique, Paris 1967. MR 0225844 (37:1435)
- 2.
- M. Auslander, M. Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, R.I., 1969. MR 0269685 (42:4580)
- 3.
- L. L. Avramov, Homological dimensions and related invariants of modules over local rings, Representations of algebra. Vol. I, II, 1-39, Beijing Norm. Univ. Press, Beijing, 2002. MR 2067368 (2005d:13022)
- 4.
- W. Bruns, J. Herzog, Cohen-Macaulay rings, Revised edition. Cambridge Studies in Advanced Mathematics, 39, Cambridge University Press, Cambridge, 1998. MR 1251956 (95h:13020)
- 5.
- L. W. Christensen, Gorenstein dimensions, Lecture Notes in Mathematics, 1747, Springer-Verlag, Berlin, 2000. MR 1799866 (2002e:13032)
- 6.
- L. W. A. Christensen, A. Frankild, H. Holm, On Gorenstein projective, injective and flat dimensions-a functorial description with applications, preprint (arXiv:math.AC/0403156 v3 17 Mar 2004).
- 7.
- E. E. Enochs, O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), no. 4, 611-633. MR 1363858 (97c:16011)
- 8.
- H. Holm, Rings with finite Gorenstein injective dimension, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1279-1283. MR 2053331 (2005a:13031)
- 9.
- L. Khatami, S. Yassemi, Gorenstein injective dimension, Bass formula and Gorenstein rings. preprint
(arXiv:math.AC/03125132 1 Jun 2004). - 10.
- C. Peskine, L. Szpiro, Dimension projective finie et cohomologie locale. Applications a la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck. Inst. Hautes Etudes Sci. Publ. Math., No. 42, (1973), 47-119. MR 0374130 (51:10330)
- 11.
- R. Takahashi, Some characterizations of Gorenstein local rings in terms of G-dimension. Acta Math. Hungar. 104 (2004), no. 4, 315-322. MR 2082781 (2005f:13015)
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Additional Information:
Ryo
Takahashi
Affiliation:
Department of Mathematics, Faculty of Science, Okayama University, 1-1, Naka 3-chome, Tsushima, Okayama 700-8530, Japan
Address at time of publication:
Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan
Email:
takahasi@math.okayama-u.ac.jp, takahasi@math.meiji.ac.jp
DOI:
10.1090/S0002-9939-06-08428-0
PII:
S 0002-9939(06)08428-0
Keywords:
G-injective dimension (Gorenstein injective dimension),
G-dimension (Gorenstein dimension).
Received by editor(s):
August 12, 2004
Received by editor(s) in revised form:
October 1, 2004, January 31, 2005, and May 31, 2005
Posted:
May 12, 2006
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2006,
American Mathematical Society
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