×
Bennis, Driss

A short survey on Gorenstein global dimension. (English) Zbl 1477.16009

Actes Rencontres C.I.R.M. 2, No. 2, 115-117 (2010).
Summary: This text gives a short overview of the recent works on Gorenstein global dimension of rings.

Cited in 1 Document

MSC:

16E10 Homological dimension in associative algebras
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)

Keywords:

global dimension of rings; Gorenstein homological dimensions of modules; Gorenstein global dimension of rings; Gorenstein rings
Cite Review PDF
Full Text: DOI Link

References:

[1] D. Bennis, \[(n, m)$-Strongly Gorenstein projective modules$, Int. Electron. J. Algebra 6 (2009), 119-13\] · Zbl 1196.16006
[2] D. Bennis, \[(n, m)$-SG rings$, AJSE-Mathematics 35 (2010), 169-17\] · Zbl 1219.16014
[3] D. Bennis, \(A note on Gorenstein global dimension of pullback rings\), Int. Electron. J. Algebra 8 (2010), 30-44. · Zbl 1253.16007
[4] D. Bennis and N. Mahdou, \(Strongly Gorenstein projective, injective, and flat modules\), J. Pure Appl. Algebra 210 (2007), 437-445. · Zbl 1118.13014
[5] D. Bennis and N. Mahdou, \(Gorenstein Global dimensions and cotorsion dimension of rings\), Comm. Algebra 37 (2009), 1709-1718. · Zbl 1172.13008
[6] D. Bennis and N. Mahdou, \(A generalization of strongly Gorenstein projective modules\), J. Algebra Appl. 8 (2009), 219-227. · Zbl 1176.16008
[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. · Zbl 1186.13007
[8] D. Bennis and N. Mahdou, \(Global Gorenstein dimensions\), Proc. Amer. Math. Soc. 138 (2010), 461-465. · Zbl 1205.16007
[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. · Zbl 1194.13008
[10] L. W. Christensen, \(Gorenstein dimensions\), Lecture Notes in Math., Springer-Verlag, Berlin (2000). · Zbl 0965.13010
[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. · Zbl 1225.13019
[12] E. E. Enochs and O. M. G. Jenda, \(Relative homological algebra\), Walter de Gruyter, Berlin (2000). · Zbl 0952.13001
[13] H. Haghighi, M. Tousi and S. Yassemi, \(Tensor products of algebra\), Commutative Algebra: Noetherian and non-Noetherian perspectives, springer-Verlag, (2011) 181-202. · Zbl 1231.13001
[14] H. Holm, \(Gorenstein homological dimensions\), J. Pure Appl. Algebra 189 (2004), 167-193. · Zbl 1050.16003
[15] E. Kirkman and J. Kuzmanovich, \(On the global dimension of fibre products\), Pacific J. Math., 134 (1988), 121-132. | · Zbl 0617.16014
[16] N. Mahdou and K. Ouarghi, \(Gorenstein dimensions in trivial ring extensions\), Commutative Algebra and Applications, W. de Gruyter, Berlin, (2009) 291-300. · Zbl 1177.13033
[17] N. Mahdou and M. Tamekkante, \(Note on (weak) Gorenstein global dimensions\), (perprint) Available from arXiv:0910.5752v1. Copyright Cellule MathDoc 2018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.