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- W2897179675 abstract "Let $mathcal{A}$ be an abelian category. For a pair $(mathcal{X},mathcal{Y}$ of classes of objects in $mathcal{A},$ we define the weak and the $(mathcal{X},mathcal{Y})$-Gorenstein relative projective objects in $mathcal{A}$. We point out that such objects generalize the usual Gorenstein projective objects and others generalizations appearing in the literature as Ding-projective, Ding-injective, $mathcal{X}$-Gorenstein projective, Gorenstein AC-projective and $G_C$-projective modules and Cohen-Macaulay objects in abelian categories. We show that the principal results on Gorenstein projective modules remains true for the weak and the $(mathcal{X},mathcal{Y}$-Gorenstein relative objects. Furthermore, by using Auslander-Buchweitz approximation theory, a relative version of Gorenstein homological dimension is developed. Finally, we introduce the notion of $mathcal{W}$-cotilting pair in the abelian category $mathcal{A}$, which is very strong connected with the cotorsion pairs related with relative Gorenstein objects in $mathcal{A}$. It is worth mentioning that the $mathcal{W}$-cotilting pairs generalize the notion of cotilting objects in the sense of L. Angeleri Hugel and F. Coelho." @default.
- W2897179675 created "2018-10-26" @default.
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- W2897179675 date "2018-10-19" @default.
- W2897179675 modified "2023-10-01" @default.
- W2897179675 title "Relative Gorenstein objects in abelian categories." @default.
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