Covers and preenvelopes by V -Gorenstein flat modules

Covers and preenvelopes by V -Gorenstein flat modules

: In this paper, we introduce and study V -Gorenstein flat modules and show the stability of the category of V -Gorenstein flat modules. We investigate the existence of V -Gorenstein flat covers and V -Gorenstein flat preenvelopes for any left R-module. Also we prove that (V -GF, V -GF⊥) is a perfect hereditary cotorsion pair in B l (R), where V -GF stands the class of V -Gorenstein flat left R-modules and B l (R) is the left Bass class. Some applications are given.

___

  • [1] Auslander M, Bridger M. Stable Module Theory. Mem Amer Math Soc 1969.
  • [2] Bouchiba S, Khaloui M. Stability of Gorenstein flat modules. Glasgow Math J 2012; 54: 169–175.
  • [3] Ding D, Chen J. Coherent ring with finite self-FP-injective dimension. Comm Algebra 1996; 24: 2963–2980.
  • [4] Enochs EE, Jenda OMG. Relative Homological Algebra. Berlin, Germany: Walter de Gruyter, 2000.
  • [5] Enochs EE, Jenda OMG. Ω -Gorenstein projective and flat covers and Ω -Gorenstein injective envelopes. Comm Algebra 2004; 32: 1453–1470.
  • [6] Enochs EE, Jenda OMG, L´opez-Ramos JA. The existence of Gorenstein flat covers. Math Scand 2004; 94: 46–62.
  • [7] Enochs EE, Jenda OMG, L´opez-Ramos JA. Covers and envelopes by V -Gorenstein modules. Comm Algebra 2005; 33: 4705–4717.
  • [8] Enochs EE, Jenda OMG, L´opez-Ramos JA. Dualizing modules and n-perfect rings. Proc Edinb Math Soc 2005; 48: 75–90.
  • [9] Enochs EE, Jenda OMG, L´opez-Ramos JA. A noncommutative generalization of Auslander’s Last Theorem. International J Math and Math Sciences 2005; 9: 1473–1480.
  • [10] Enochs EE, L´opez-Ramos JA. Kaplansky classes. Rend Sem Math Univ Padova 2002; 107: 67–79.
  • [11] Esmkhani MA, Tousi M. Gorenstein homological dimensions and Auslander categories. J Algebra 2007; 308: 321– 329.
  • [12] Holm H. Gorenstein homological dimensions. J Pure Appl Algebra 2004; 189: 167–193.
  • [13] Holm H, J ø rgensen P. Cotorsion pairs induced by duality pairs. J Commut Algebra 2009; 1: 621–633.
  • [14] Holm H, White D. Foxby equivalence over associative rings. J Math Kyoto Univ 2007; 47: 781–808.
  • [15] Mao L, Ding N. Envelopes and covers by modules of finite FP-injective and flat dimensions. Comm Algebra 2007; 35: 833–849.
  • [16] Yang X, Liu Z. Ω -Gorenstein projective, injective and flat modules. Algebra Colloq 2011; 18: 273–288.
  • [17] Yang X, Liu Z. V -Gorenstein projective, injective and flat modules. Rocky Mt J Math 2012; 42: 2075–2098.