• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1031-1048
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• 2019

In this paper we study recollements of abelian categories and balanced pairs. The main results are: recollements induce new balanced pairs from the middle category; the resolution dimensions are bounded under certain conditions. As an application, the resolution dimensions with respect to cotilting objects of abelian categories involved in recollements are recovered.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.53-71
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• 2018

In this paper, we provide two different descriptions for a relative derived category with respect to a subcategory ${\mathcal{X}}$ of an abelian category ${\mathcal{A}}$. First, we construct an exact model structure on certain exact category which has as its homotopy category the relative derived category of ${\mathcal{A}}$. We also show that a relative derived category is equivalent to homotopy category of certain complexes. Moreover, we investigate the existence of certain recollements in such categories.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.405-423
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• 2023

Let (𝓛, 𝒜) be a complete duality pair. We give some equivalent characterizations of Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures and recollements associated to them.