| Orthogonal Classes and Relative Gorenstein Modules |
| Received:February 06, 2023 Revised:July 07, 2023 |
| Key Words:
Gorenstein module orthogonal class duality pair Mittag-Leffler condition
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| Fund Project:Supported by Qinglan Project of Jiangsu Province (Grant No.2022), the National Natural Science Foundation of China (Grant No.11701408) and Jiangsu Provincial Government Scholarship Program. |
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| Abstract: |
| In this paper, we study the relations between the class of $\mathcal{A}$-Gorenstein projective modules and the left orthogonal class of $\mathcal{A}$, also the relations between the class of $\mathcal{A}$-Gorenstein injective modules and the right orthogonal class of $\mathcal{A}$. Some functor characterizations of $\mathcal{A}$-Gorenstein projective modules and $\mathcal{A}$-Gorenstein injective modules are obtained. Using the notion of complete duality pair, we discuss the relations between $\mathcal{A}$-Gorenstein projective modules and $\mathcal{B}$-Gorenstein flat modules. Some known results are generalized. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.01.004 |
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