A short survey on Gorenstein global dimension

Driss Bennis[1]

  • [1] Department of Mathematics, Faculty of Science, University Mohammed V, Rabat, Morocco

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 2, page 115-117
  • ISSN: 2105-0597

Abstract

top
This text gives a short overview of the recent works on Gorenstein global dimension of rings.

How to cite

top

Bennis, Driss. "A short survey on Gorenstein global dimension." Actes des rencontres du CIRM 2.2 (2010): 115-117. <http://eudml.org/doc/196290>.

@article{Bennis2010,
abstract = {This text gives a short overview of the recent works on Gorenstein global dimension of rings.},
affiliation = {Department of Mathematics, Faculty of Science, University Mohammed V, Rabat, Morocco},
author = {Bennis, Driss},
journal = {Actes des rencontres du CIRM},
keywords = {Global dimension of rings; Gorenstein homological dimensions of modules; Gorenstein global dimension of rings; Gorenstein rings; pullback rings; Gorenstein homological dimension; divisorial ideals; divisorial rings; Gorenstein projective modules},
language = {eng},
number = {2},
pages = {115-117},
publisher = {CIRM},
title = {A short survey on Gorenstein global dimension},
url = {http://eudml.org/doc/196290},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Bennis, Driss
TI - A short survey on Gorenstein global dimension
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 115
EP - 117
AB - This text gives a short overview of the recent works on Gorenstein global dimension of rings.
LA - eng
KW - Global dimension of rings; Gorenstein homological dimensions of modules; Gorenstein global dimension of rings; Gorenstein rings; pullback rings; Gorenstein homological dimension; divisorial ideals; divisorial rings; Gorenstein projective modules
UR - http://eudml.org/doc/196290
ER -

References

top
  1. D. Bennis, ( n , m ) -Strongly Gorenstein projective modules, Int. Electron. J. Algebra 6 (2009), 119–133. Zbl1196.16006MR2520962
  2. D. Bennis, ( n , m ) -SG rings, AJSE-Mathematics 35 (2010), 169–178. Zbl1219.16014MR2792504
  3. D. Bennis, A note on Gorenstein global dimension of pullback rings, Int. Electron. J. Algebra 8 (2010), 30–44. Zbl1253.16007MR2660539
  4. D. Bennis and N. Mahdou, Strongly Gorenstein projective, injective, and flat modules, J. Pure Appl. Algebra 210 (2007), 437–445. Zbl1118.13014MR2320007
  5. D. Bennis and N. Mahdou, Gorenstein Global dimensions and cotorsion dimension of rings, Comm. Algebra 37 (2009), 1709–1718. Zbl1172.13008MR2526333
  6. D. Bennis and N. Mahdou, A generalization of strongly Gorenstein projective modules, J. Algebra Appl. 8 (2009), 219–227. Zbl1176.16008MR2514856
  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. Zbl1186.13007MR2577139
  8. D. Bennis and N. Mahdou, Global Gorenstein dimensions, Proc. Amer. Math. Soc. 138 (2010), 461–465. Zbl1205.16007MR2557164
  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. Zbl1194.13008MR2665200
  10. L. W. Christensen, Gorenstein dimensions, Lecture Notes in Math., Springer-Verlag, Berlin (2000). Zbl0965.13010MR1799866
  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. Zbl1225.13019MR2762509
  12. E. E. Enochs and O. M. G. Jenda, Relative homological algebra, Walter de Gruyter, Berlin (2000). Zbl1238.13002MR1753146
  13. H. Haghighi, M. Tousi and S. Yassemi, Tensor products of algebra, Commutative Algebra: Noetherian and non-Noetherian perspectives, springer-Verlag, (2011) 181–202. Zbl1231.13001MR2762511
  14. H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), 167–193. Zbl1050.16003MR2038564
  15. E. Kirkman and J. Kuzmanovich, On the global dimension of fibre products, Pacific J. Math., 134 (1988), 121–132. Zbl0617.16014MR953503
  16. N. Mahdou and K. Ouarghi, Gorenstein dimensions in trivial ring extensions, Commutative Algebra and Applications, W. de Gruyter, Berlin, (2009) 291–300. Zbl1177.13033MR2606294
  17. N. Mahdou and M. Tamekkante, Note on (weak) Gorenstein global dimensions, (perprint) Available from arXiv:0910.5752v1. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.