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In this paper, the relative derived categories with respect to $${\mathcal {X}}$$ -Gorenstein projective modules and $${\mathcal {Y}}$$ -Gorenstein injective modules are introduced to unify Gorestein derived categories and Ding… Click to show full abstract
In this paper, the relative derived categories with respect to $${\mathcal {X}}$$ -Gorenstein projective modules and $${\mathcal {Y}}$$ -Gorenstein injective modules are introduced to unify Gorestein derived categories and Ding derived categories in certain sense. A triangle-equivalence and description of morphisms in such relative derived categories are given. We also discuss a generalized Tate cohomology and obtain Avramov–Martsinkovsky exact sequences. Finally, some applications are obtained.
Journal Title: Bulletin of The Iranian Mathematical Society
Year Published: 2021
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