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Global Gorenstein dimensions
Author(s):
Driss
Bennis;
Najib
Mahdou
Journal:
Proc. Amer. Math. Soc.
138
(2010),
461-465.
MSC (2000):
Primary 16E05, 16E10, 16E30, 16E65
Posted:
September 28, 2009
MathSciNet review:
2557164
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Abstract:
In this paper, we prove that the global Gorenstein projective dimension of a ring  is equal to the global Gorenstein injective dimension of  and that the global Gorenstein flat dimension of  is smaller than the common value of the terms of this equality.
References:
-
- 1.
- D. Bennis and N. Mahdou, Strongly Gorenstein projective, injective, and flat modules, J. Pure Appl. Algebra 210 (2007), 437-445. MR 2320007 (2008d:13020)
- 2.
- D. Bennis, N. Mahdou and K. Ouarghi, Rings over which all modules are strongly Gorenstein projective. Accepted for publication in Rocky Mountain Journal of Mathematics. Available from arXiv:0712.0127v2.
- 3.
- L. W. Christensen, Gorenstein dimensions, Lecture Notes in Math., 1747, Springer-Verlag, Berlin (2000). MR 1799866 (2002e:13032)
- 4.
- E. E. Enochs and O. M. G. Jenda, Relative homological algebra, Walter de Gruyter, Berlin-New York (2000). MR 1753146 (2001h:16013)
- 5.
- R. M. Fossum, P. A. Griffith and I. Reiten, Trivial extensions of abelian categories, Lecture Notes in Math., 456, Springer-Verlag, Berlin (1975). MR 0389981 (52:10810)
- 6.
- H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), 167-193. MR 2038564 (2004k:16013)
- 7.
- H. Holm, Rings with finite Gorenstein injective dimension, Proc. Amer. Math. Soc. 132 (2004), 1279-1283. MR 2053331 (2005a:13031)
- 8.
- H. Holm, Gorenstein Homological Algebra, Ph.D. thesis, University of Copenhagen, Denmark (2004).
- 9.
- A. V. Jategaonkar, A counter-example in ring theory and homological algebra, J. Algebra 12 (1969), 418-440. MR 0240131 (39:1485)
- 10.
- C. U. Jensen, On the vanishing of
 , J. Algebra 15 (1970), 151-166. MR 0260839 (41:5460) - 11.
- W. K. Nicholson and M. F. Youssif, Quasi-Frobenius Rings, Cambridge University Press (2003). MR 2003785 (2005b:16042)
- 12.
- J. Rotman, An Introduction to Homological Algebra, Academic Press, New York (1979). MR 538169 (80k:18001)
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Additional Information:
Driss
Bennis
Affiliation:
Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco
Email:
driss_bennis@hotmail.com
Najib
Mahdou
Affiliation:
Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco
Email:
mahdou@hotmail.com
DOI:
10.1090/S0002-9939-09-10099-0
PII:
S 0002-9939(09)10099-0
Keywords:
Global dimension of rings,
weak global dimension of rings,
Gorenstein homological dimensions of modules,
Gorenstein global dimension of rings,
weak Gorenstein global dimension of rings
Received by editor(s):
August 25, 2008,
Received by editor(s) in revised form:
June 1, 2009
Posted:
September 28, 2009
Dedicated:
Dedicated to our advisor, Salah-Eddine Kabbaj
Communicated by:
Birge Huisgen-Zimmermann
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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