Volume 2, Issue 1, April 2018, pp 20-30
Lingling Tan
Department of Electronic Engineering, Jiangsu Province Nanjing Engineering Vocational College, 211135 Nanjing, China.
In this paper, we introduce the notion of (strongly) 𝘎𝘍-projective modules. We show that a module is projective if and only if it is 𝘎𝘍-projective and its Gorenstein flat dimension is at most 1, if and only if it is strongly 𝘎𝘍-projective and Gorenstein flat. Moreover, we investigate (global) 𝘎𝘍-projective dimensions of modules and rings, and some applications are presented.
Gorenstein flat module, 𝘎𝘍-projective module, (global) 𝘎𝘍-projective dimension.
1. N. Ding, Y. Li and L. Mao, Strongly Gorenstein flat modules, J. Aust. Math. Soc. 86 (2009), 323-338.
2. E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, Walter de Gruyter, Berlin, 2000.
3. Z. Gao, On GI-injective modules, Comm. Algebra, 40 (2012), 3841-3858.
4. Z. Gao, On GI-flat modules and dimensions, J. Korean Math. Soc. 50 (2013), no. 1, 203-218.
5. J. Gillespie, Model structures on modules over Ding-Chen rings, Homology, Homotopy Appl. 12 (2010), 61-73.
6. H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), 167-193.
7. T. Ishikawa, On injective modules and flat modules, J.Math. Soc. Japan 17 (1965), no. 3, 291-296.
8. Y. Iwanaga, On rings with finite self-injective dimension, Comm. Algebra 7 (1979), no. 4, 393-414.
9. Y. Iwanaga, On rings with finite self-injective dimension II, Tsukuba J. Math. 4 (1980), no. 1, 107-113.
10. L. X. Mao and N. Q. Ding, Gorenstein FP-injective and Gorenstein at modules, J. Algebra Appl. 7 (2008), 491-506.
11. J.J. Rotman, An introduction to homological algebra, 2nd ed. Springer, 2009.
12. T. Zhao, DP-projective modules and dimensions, Int. Electron. J. Algebra 15 (2014), 101-116.
13. T. Zhao and Y. Xu, On right orthogonal classes and cohomology over Ding-Chen rings, Bull. Malays. Math. Sci. Soc. 40 (2017), 617-634.
