Turkish Journal of Mathematics
DOI
10.3906/mat-2004-98
Abstract
For a class of $R$-modules $\mathcal{X}$ containing all projective $R$-modules, the $\mathcal{X}$-Gorenstein projective $R$-modules vary from projective to Gorenstein projective $R$-modules. We characterize the rings over which the left global $\mathcal{X}$-Gorenstein projective dimensions are finite. If further $\mathcal{Y}$ contains all injective $R$-modules, we show the existence of a new left global Gorenstein dimension of $R$ with respect to $\mathcal{X}$ and $\mathcal{Y}$ satisfying proper conditions. As an application we characterize Ding-Chen rings by this new global Gorenstein dimension and show the existence of Ding-Chen rings with infinite global Gorenstein dimension. We also show the existence of $\mathcal{X}$-Gorenstein projective precovers for a large class of rings.
Keywords
Ding-Chen rings, Ding projective (injective) modules, global Gorenstein dimensions, precovers, $\mathcal{X}$-Gorenstein projective modules
First Page
1768
Last Page
1782
Recommended Citation
YU, BIN
(2020)
"On $\mathcal{X}$-Gorenstein projective dimensions and precovers,"
Turkish Journal of Mathematics: Vol. 44:
No.
5, Article 19.
https://doi.org/10.3906/mat-2004-98
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss5/19
