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Turkish Journal of Mathematics

Authors

BIN YU

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.

First Page

1768

Last Page

1782

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Mathematics Commons

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