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Yongyun Qin

Publications and source records attributed to Yongyun Qin.

16 recordsLinked to original sources
arXiv2026

Quasi-projective dimension and Gorenstein projective dimension

Gheibi, Jorgensen and Takahashi recently introduced the quasi-projective dimension, a homological invariant that extends the classical projective dimension. In this paper, we investigate this invariant from the perspective of Gorenstein homological algebra. First, we show that the quasi-projective dimension coincides with the Gorenstein projective dimension under certain conditions. Second, we introduce and study the quasi-Gorenstein projective dimension as a Gorenstein analogue of the quasi-projective dimension.

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arXiv2026

Gorenstein flat-cotorsion modules over tensor rings

Let $T_R(M)$ be a tensor ring, where $R$ is a ring and $M$ is an $N$-nilpotent $R$-bimodule. Under certain conditions, we characterize the Gorenstein flat-cotorsion modules over $T_R(M)$, showing that a $T_R(M)$-module $(X, u)$ is Gorenstein flat-cotorsion if and only if $u$ is monomorphic and $\Coker u$ is a Gorenstein flat-cotorsion $R$-module. As applications, we describe the Gorenstein flat-cotorsion modules over some trivial extension rings and Morita context rings.

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arXiv2026

Gluing of cotorsion pairs via recollements of abelian categories

Let $( \mathcal{A^{'}},\mathcal{A},\mathcal{A^{''}},i^\ast,i_\ast,i^!,j_!,j^\ast,j_\ast)$ be a recollement of abelian categories. Suppose that we are given two cotorsion pairs $({\mathcal{U^{'}}},\mathcal{V{'}})$ and $({\mathcal{U}^{''}},{\mathcal{V}^{''}})$ in $\mathcal{A}^{'}$ and $\mathcal{A}^{''}$, respectively. We construct two cotorsion pairs $(^{\bot}{\mathcal{N}_{\mathcal{V^{''}}}^{\mathcal{V^{'}}}},\mathcal{N}_{\mathcal{V^{''}}}^{\mathcal{V^{'}}})$ and $(\mathcal{M}_{\mathcal{U^{''}}}^{\mathcal{U^{'}}}, ({\mathcal{M}_{\mathcal{U^{''}}}^{\mathcal{U^{'}}}})^\bot)$ in $\mathcal{A}$. Moreover, we provide a sufficient condition for these two cotorsion pairs to coincide, and we investigate the heredity and completeness of $(\mathcal{M}_{\mathcal{U^{''}}}^{\mathcal{U^{'}}},\mathcal{N}_{\mathcal{V^{''}}}^{\mathcal{V^{'}}})$. These results are applied to construct new cotorsion pairs in Morita rings. In the course of proof, we introduce a specific constraint on recollements of abelian categories, requiring $\varepsilon_P$ to be a monomorphism for any projective $P \in \mathcal{A}$, with $\varepsilon: j_!j^* \to \mathrm{id}_{\mathcal{A}}$ being the counit of $(j_!, j^*)$. Such recollements enjoy rich homological properties and hence might be of independent interest.

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arXiv2025

Gorenstein projective objects over cleft extensions

In this paper we introduce compatible cleft extensions of abelian categories, and we prove that if $(\mathcal{B},\mathcal{A}, e,i,l)$ is a compatible cleft extension, then both the functor $l$ and the left adjoint of $i$ preserve Gorenstein projective objects. Moreover, we give some necessary conditions for an object of $\mathcal{A}$ to be Gorenstein projective, and we show that these necessary conditions are also sufficient in some special case. As applications, we unify some known results on the description of Gorenstein projective modules over triangular matrix rings, Morita context rings with zero homomorphisms and $θ$-extensions.

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arXiv2025

ICE-closed subcategories and epibricks over recollements

Let $( \mathcal{A^{'}},\mathcal{A},\mathcal{A^{''}},i^\ast,i_\ast,i_!,j_!,j^\ast,j_\ast)$ be a recollement of abelian categories. We proved that every ICE-closed subcategory (resp. epibrick, monobrick) in $\mathcal{A^{'}}$ or $\mathcal{A^{''}}$ can be extended to an ICE-closed subcategories (resp. epibrick, monobrick) in $\mathcal{A}$, and the assignment $\mathcal{C}\mapsto j^*(\mathcal{C})$ defines a bijection between certain ICE-closed subcategories in $\mathcal{A}$ and those in $\mathcal{A}''$. Moreover, the ICE-closed subcategory $\mathcal{C}$ of $\mathcal{A}$ containing $i_\ast(\mathcal{A^{'}})$ admits a new recollement relative to ICE-closed subcategories $\mathcal{A^{'}}$ and $j^\ast(\mathcal{C})$ which induced from the original recollement when $j_!{j^\ast(\mathcal{C})}\subset\mathcal{C}$.

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arXiv2024

Categorical properties and homological conjectures for bounded extensions of algebras

An extension $B\subset A$ of finite dimensional algebras is bounded if the $B$-$B$-bimodule $A/B$ is $B$-tensor nilpotent, its projective dimension is finite and $\mathrm{Tor}_i^B(A/B, (A/B)^{\otimes_B j})=0$ for all $i, j\geq 1$. We show that for a bounded extension $B\subset A$, the algebras $A$ and $B$ are singularly equivalent of Morita type with level. Additionally, under mild conditions, their stable categories of Gorenstein projective modules and Gorenstein defect categories are equivalent, respectively. Some homological conjectures are also investigated for bounded extensions, including Auslander-Reiten conjecture, finististic dimension conjecture, Fg condition, Han's conjecture, and Keller's conjecture. Applications to trivial extensions and triangular matrix algebras are given. In course of proof, we give some handy criteria for a functor between module categories to induce triangle functors between stable categories of Gorenstein projective modules and Gorenstein defect categories, which generalise some known criteria, and hence might be of independent interest.

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arXiv2024

Singular equivalences induced by ring extensions

Let $B \subseteq A$ be an extension of finite dimensional algebras. We provide a sufficient condition for the existence of triangle equivalences of singularity categories (resp. Gorenstein defect categories) between $A$ and $B$. This result is applied to trivial extensions, Morita rings and triangular matrix algebras to give several reduction methods on singularity categories and Gorenstein defect categories of algebras.

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arXiv2023

A note on singularity categories and triangular matrix algebras

Let $Λ= \left[\begin{array}{cc} A & 0 \\ M & B \end{array}\right] $ be an Artin algebra and $_BM_A$ a $B$-$A$-bimodule. We prove that there is a triangle equivalence $D_{sg}(Λ) \cong D_{sg}(A)\coprod D_{sg}(B)$ between the corresponding singularity categories if $_BM$ is semi-simple and $M_A$ is projective. As a result, we obtain a new method for describing the singularity categories of certain bounded quiver algebras.

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arXiv2022

Eventually homological isomorphisms and Gorenstein projective modules

We prove that a certain eventually homological isomorphism between module categories induces a triangle equivalence between their singularity categories, Gorenstein defect categories and the stable categories of Gorenstein projective modules. Further, we show that Auslander-Reiten conjecture and Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms. Applying the results to arrow removal and vertex removal, we describe the Gorenstein projective modules over some non-monomial algebras, and we verify the Auslander-Reiten conjecture for certain algebras.

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arXiv2021

Reduction techniques of singular equivalences

It is shown that a singular equivalence induced by tensoring with a suitable complex of bimodules defines a singular equivalence of Morita type with level, in the sense of Wang. This result is applied to homological ideals and idempotents to produce new reduction techniques for testing the properties of syzygy-finite and injectives generation of finite dimensional algebras over a field.

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arXiv2020

Singular equivalences and Auslander-Reiten conjecture

Auslander-Reiten conjecture, which says that an Artin algebra does not have any non-projective generator with vanishing self-extensions in all positive degrees, is shown to be invariant under certain singular equivalences induced by adjoint pairs, which occur often in matrix algebras, recollements and change of rings. Accordingly, several reduction methods are established to study this conjecture.

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arXiv2020

Recollements, Cohen-Macaulay Auslander algebras and Gorenstein projective conjecture

It is shown that a 4-recollement of derived categories of CM-finite algebras induces a 2-recollement of the corresponding Cohen-Macaulay Auslander algebras, which generalises the main theorem of Pan [S. Y. Pan, Derived equivalences for Cohen-Macaulay Auslander algebras, J. Pure Appl. Algebra 216 (2012), 355{363]. Moreover, both Auslander- Reiten conjecture and Gorenstein projective conjecture are shown invariant under 3 (or 4)-recollement of unbounded derived categories of algebras.

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arXiv2018

Eventually homological isomorphisms in recollements of derived categories

For a recollement $(\mathcal{D}B,\mathcal{D}A,\mathcal{D}C)$ of derived categories of algebras, we investigate when the functor $j^*:\mathcal{D}A\rightarrow\mathcal{D}C$ is an eventually homological isomorphism. In this context, we compare the algebras $A$ and $C$ with respect to Gorensteinness, singularity categories and the finite generation condition Fg for the Hochschild cohomology. The results are applied to stratifying ideals, triangular matrix algebras and derived discrete algebras.

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arXiv2016

Recollements and homological dimensions

We investigate the behavior of the homological dimensions under recollements of derived categories of algebras. In particular, we establish a series of new bounds among the selfinjective dimension or $ϕ$-dimension of the algebras linked by recollements of derived module categories.

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arXiv2014

Reducing homological conjectures by n-recollements

n-recollements of triangulated categories and n-derived-simple algebras are introduced. The relations between the n-recollements of derived categories of algebras and the Cartan determinants, homological smoothness and Gorensteinness of algebras respectively are clarified. As applications, the Cartan determinant conjecture is reduced to 1-derived-simple algebras, and the Gorenstein symmetry conjecture is reduced to 2-derived-simple algebras.

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