203
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

On Balance for Relative Homology

, , &
Pages 4262-4276 | Received 16 Dec 2014, Published online: 03 Jun 2016

REFERENCES

  • Auslander, M., Buchweitz, R. O. (1989). The Homological theory of maximal Cohen–Macaulay approximations. Mem. Soc. Math. France 38:5–37.
  • Avramov, L. L., Martsinkovsky, A. (2002). Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension. Proc. Lond. Math. Soc. 85:393–440.
  • Butler, M. C. R., Horrocks, G. (1961/1962). Classes of extensions and resolutions. Philos. Trans. Roy. Soc. Lond. Ser. A. 254:155–222.
  • Christensen, L. W. (2001). Semi-dualizing complexes and their Auslander categories. Trans. Amer. Math. Soc. 353:1839–1883.
  • Christensen, L. W., Frankild, A., Holm, H. (2006). On Gorenstein projective, injective and flat dimensions −A functorial description with applications. J. Algebra 302:231–279.
  • Di, Z. X., Zhang, X. X., Liu, Z. K., Chen, J. L. (2014). Relative and Tate homology with respect to semidualizing modules. J. Algebra Appl. 10:1261–1282.
  • Eilenberg, S., Moore, J. C. (1965). Foundations of relative homological algebra. Mem. Am. Math. Soc. 55:39.
  • Emmanouil, I. (2012). On the finiteness of Gorenstein homological dimensions. J. Algebra 372:376–396.
  • Enochs, E. E., Jenda, O. M. G. (2000). Relative Homological Algebra. De Gruyter Expositions in Mathematics, Vol. 30. New York: Walter De Gruyter.
  • Enochs, E. E., Yassemi, S. (2004). Foxby equivalence and cotorsion theories relative to semi-dualizing modules. Math. Scand. 95:33–43.
  • Foxby, H.-B. (1972). Gorenstein modules and related modules. Math. Scand. 31:267–284.
  • Geng, Y. X., Ding, N. Q. (2011). 𝒲-Gorenstein modules. J. Algebra 325:132–146.
  • Golod, E. S. (1984). G-dimension and generalized perfect ideals. Trudy. Mat. Inst. Steklov. 165:62–66.
  • Holm, H. (2004). Gorenstein derived functors. Proc. Amer. Math. Soc. 132:1913–1923.
  • Holm, H. (2004). Gorenstein homological dimensions. J. Pure Appl. Algebra 189:167–193.
  • Holm, H., Jøgensen, P. (2006). Semi-dualizing modules and related Gorenstein homological dimensions. J. Pure Appl. Algebra 205:423–445.
  • Holm, H., White, D. (2007). Foxby equivalence over associative rings. J. Math. Kyoto Univ. 47:781–808.
  • Hu, J. S., Zhang, D. D., Ding, N. Q. (2014). Gorenstein right derived functors of − ⊗ −with respect to semidualizing modules. Comm. Algebra 42:3205–3219.
  • Huang, Z. Y. (2013). Proper resolutions and Gorenstein categories. J. Algebra 393:142–169.
  • Jorgensen, D. A., Leuschke, G. J., Sather-Wagstaff, S. (2012). Presentations of rings with non-trivial semidualizing modules. Collect. Math. 63:165–180.
  • Liu, Z. F., Huang, Z. Y., Xu, A. M. (2013). Gorenstein projective dimension relative to a semidualizing bimodule. Comm. Algebra 41:1–18.
  • Liang, L., Yang, G. (2013). Balance for Tate cohomology with respect to semidualzing modules. J. Aust. Math. Soc. 95:223–240.
  • Salimi, M., Sather-Wagstaff, S., Tavasoli, E., Yassemi, S. (2014). Relative Tor functors with respect to a semidualizingmodule. Algebr. Represent Theor. 17:103–120.
  • Sather-Wagstaff, S., Sharif, T., White, D. (2011). AB-contexts and stability for Gorenstein flat modules with respect to semidualizing modules. Algebr Represent Theor. 14:403–428.
  • Sather-Wagstaff, S., Sharif, T., White, D. (2010). Comparison of relative cohomology theories with respect to semidualizing modules. Math. Z. 264:571–600.
  • Sather-Wagstaff, S., Sharif, T., White, D. (2008). Gorenstein cohomology in abelian categories. J. Math. Kyoto Univ. 48:571–596.
  • Vasconcelos, W. V. (1974). Divisor Theory in Module Categories. Amsterdam: North-Holland Publishing Co., North-Holland Mathematics Studies, No. 14, Notas de Matemática No. 53. [Notes on Mathematics, No. 53].
  • White, D. (2010). Gorenstein projective dimension with respect to a semidualizing module. J. Commut. Algebra 2:111–137.
  • Zhang, D. D., Ouyang, B. Y. (2011). Semidualizing modules and related modules. J. Algebra Appl. 10:1261–1282.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.