This text gives a short overview of the recent works on Gorenstein global dimension of rings.
Mots clés: Global dimension of rings; Gorenstein homological dimensions of modules; Gorenstein global dimension of rings; Gorenstein rings
@article{ACIRM_2010__2_2_115_0,
author = {Driss Bennis},
title = {A short survey on Gorenstein global dimension},
journal = {Actes des rencontres du CIRM},
publisher = {CIRM},
volume = {2},
number = {2},
year = {2010},
pages = {115-117},
doi = {10.5802/acirm.46},
language = {en},
url = {acirm.centre-mersenne.org/item/ACIRM_2010__2_2_115_0/}
}
Bennis, Driss. A short survey on Gorenstein global dimension. Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 115-117. doi : 10.5802/acirm.46. https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_115_0/
[1] D. Bennis, -Strongly Gorenstein projective modules, Int. Electron. J. Algebra 6 (2009), 119–133.
[2] D. Bennis, -SG rings, AJSE-Mathematics 35 (2010), 169–178.
[3] D. Bennis, A note on Gorenstein global dimension of pullback rings, Int. Electron. J. Algebra 8 (2010), 30–44.
[4] D. Bennis and N. Mahdou, Strongly Gorenstein projective, injective, and flat modules, J. Pure Appl. Algebra 210 (2007), 437–445.
[5] D. Bennis and N. Mahdou, Gorenstein Global dimensions and cotorsion dimension of rings, Comm. Algebra 37 (2009), 1709–1718.
[6] D. Bennis and N. Mahdou, A generalization of strongly Gorenstein projective modules, J. Algebra Appl. 8 (2009), 219–227.
[7] D. Bennis and N. Mahdou, Global Gorenstein dimensions of polynomial rings and of direct products of rings, Houston J. Math. 35 (2009), 1019–1028.
[8] D. Bennis and N. Mahdou, Global Gorenstein dimensions, Proc. Amer. Math. Soc. 138 (2010), 461–465.
[9] D. Bennis, N. Mahdou and K. Ouarghi, Rings over which all modules are strongly Gorenstein projective, Rocky Mountain J. Math. 40 (2010), 749–759.
[10] L. W. Christensen, Gorenstein dimensions, Lecture Notes in Math., Springer-Verlag, Berlin (2000).
[11] L. W. Christensen, H-B. Foxby and H. Holm, Beyond Totally Reflexive Modules and Back. A Survey on Gorenstein Dimensions, Commutative Algebra: Noetherian and non-Noetherian perspectives, Springer-Verlag, (2011) 101–143.
[12] E. E. Enochs and O. M. G. Jenda, Relative homological algebra, Walter de Gruyter, Berlin (2000).
[13] H. Haghighi, M. Tousi and S. Yassemi, Tensor products of algebra, Commutative Algebra: Noetherian and non-Noetherian perspectives, springer-Verlag, (2011) 181–202.
[14] H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), 167–193.
[15] E. Kirkman and J. Kuzmanovich, On the global dimension of fibre products, Pacific J. Math., 134 (1988), 121–132.
[16] N. Mahdou and K. Ouarghi, Gorenstein dimensions in trivial ring extensions, Commutative Algebra and Applications, W. de Gruyter, Berlin, (2009) 291–300.
[17] N. Mahdou and M. Tamekkante, Note on (weak) Gorenstein global dimensions, (perprint) Available from arXiv:0910.5752v1.