Proceedings of the American Mathematical Society

Author(s): Henrik Holm
Journal: Proc. Amer. Math. Soc. 132 (2004), 1913-1923.
MSC (2000): Primary 13D02, 13D05, 13D07, 13H10, 16E05, 16E10, 16E30
Posted: February 13, 2004
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Abstract: Over any associative ring

it is standard to derive $\mathrm{Hom}_R(-,-)$ using projective resolutions in the first variable, or injective resolutions in the second variable, and doing this, one obtains $\mathrm{Ext}_R^n(-,-)$ in both cases. We examine the situation where projective and injective modules are replaced by Gorenstein projective and Gorenstein injective ones, respectively. Furthermore, we derive the tensor product $-\otimes_R-$ using Gorenstein flat modules.

1.: M. Auslander, Anneaux de Gorenstein et torsion en algèbre commutative, Séminaire d'algèbre commutative 1966/67, notes by M. Mangeney, C. Peskine and L. Szpiro, École Normale Supérieure de Jeunes Filles, Paris, Secrétariat mathématique, 1967. MR 37:1435
2.: M. Auslander and M. Bridger, Stable module theory, Mem. Amer. Math. Soc. 94, American Mathematical Society, Providence, RI, 1969. MR 42:4580
3.: L. L. Avramov and A. Martsinkovsky, Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension, Proc. London Math. Soc. 85, Part 2 (2002), . MR 2003g:16009
4.: L. W. Christensen, Gorenstein dimensions, Lecture Notes in Math. 1747, Springer-Verlag, Berlin, 2000. MR 2002e:13032
5.: E. E. Enochs and O. M. G. Jenda, Balanced functors applied to modules, J. Algebra 92 (1985), . MR 86h:16025
6.: E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), . MR 97c:16011
7.: E. E. Enochs and O. M. G. Jenda, Gorenstein balance of hom and tensor, Tsukuba J. Math. 19, No. 1 (1995), . MR 97a:16019
8.: E. E. Enochs and O. M. G. Jenda, Gorenstein injective and flat dimensions, Math. Japonica 44, No. 2 (1996), . MR 97k:13019
9.: E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter Expositions in Math. 30, Walter de Gruyter, Berlin, 2000. MR 2001h:16013
10.: L. Gruson and M. Raynaud, Critères de platitude et de projectivité. Techniques de ``platification'' d'un module, Invent. Math. 13 (1971), . MR 46:7219
11.: R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York-Heidelberg, 1977. MR 57:3116
12.: H. Holm, Gorenstein homological dimensions, J. Pure and Appl. Algebra (to appear).
13.: C. U. Jensen, On the vanishing of $\varprojlim^{(i)}$ , J. Algebra 15 (1970), . MR 41:5460
14.: C. A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, Cambridge, 1994. MR 95f:18001
15.: J. Xu, Flat covers of modules, Lecture Notes in Math. 1634, Springer-Verlag, Berlin, 1996. MR 98b:16003

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