37 citations · 132 across the 19 of their papers we have counts for
21 papers
Finiteness of homological dimensions in triangulated categories
Hongxing Chen, Xiaohu Chen, Jinbi Zhang
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existenc…
Quasi-projective dimensions of complexes over rings
Hongxing Chen, Jiangsheng Hu, Xiaoyan Yang
Quasi-projective dimension of modules over associative rings is generalized in this paper to the one of complexes of modules. Basic properties of this dimension are established, in…
Properties of quasi-projective dimension over abelian categories
Hongxing Chen, Xiaohu Chen, Mengge Liu
Quasi-projective dimension was introduced by Gheibi, Jorgensen and Takahashi to generalize the Auslander-Buchsbaum formula and the depth formula in commutative algebra. In this pap…
Virtually Gorenstein algebras of infinite dominant dimension
Hongxing Chen, Changchang Xi
Motivated by understanding the Nakayama conjecture which states that algebras of infinite dominant dimension should be self-injective, we study self-orthogonal modules with virtual…
Derived equivalences for mirror-reflective algebras
Hongxing Chen, Changchang Xi
We show that the construction of mirror-reflective algebras inherits derived equivalences of gendo-symmetric algebras. More precisely, suppose A and B are gendo-symmetric algebras…
Mirror-reflective algebras and Tachikawa's second conjecture
Hongxing Chen, Ming Fang, Changchang Xi
Given an algebra with an idempotent, we introduce two procedures to construct families of new algebras, termed mirror-reflective algebras and reduced mirror-reflective algebras. We…
Resolving dualities and applications to homological invariants
Hongxing Chen, Jiangsheng Hu
Dualities of resolving subcategories of finitely generated modules over Artin algebras are characterized as dualities with respect to Wakamatsu tilting bimodules. By restriction of…
Homological theory of orthogonal modules
Hongxing Chen, Changchang Xi
Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a finite-dimensional self-injective algebra is projective. This conjecture is an important…
Symmetric subcategories, tilting modules and derived recollements
Hongxing Chen, Changchang Xi
For any good tilting module over a ring , there exists an -symmetric subcategory of a module category such that the derived category of the endomorphism rin…
Derived decompositions of abelian categories I
Hongxing Chen, Changchang Xi
Derived decompositions of abelian categories are introduced in internal terms of abelian subcategories to construct semi-orthogonal decompositions (or Bousfield localizations, or h…
Rigidity dimension - a homological dimension measuring resolutions of algebras by algebras of finite global dimension
Hongxing Chen, Ming Fang, Otto Kerner +2
A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finit…
Ortho-symmetric modules, Gorenstein algebras and derived equivalences
Hongxing Chen, Steffen Koenig
A new homological symmetry condition is exhibited that extends and unifies several recently defined and widely used concepts. Applications include general constructions of tilting…
Dominant dimensions, derived equivalences and tilting modules
Hongxing Chen, Changchang Xi
The Nakayama conjecture states that an algebra of infinite dominant dimension should be self-injective. Motivated by understanding this conjecture in the context of derived categor…
Recollements of derived categories III: finitistic dimensions
Hongxing Chen, Changchang Xi
In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among t…
Recollements of derived categories II: Algebraic K-theory
Hongxing Chen, Changchang Xi
For a recollement of derived module categories of rings, we provide sufficient conditions to guarantee the additivity formula of higher algebraic K-groups of the rings involved, an…
Algebraic K-theory of endomorphism rings
Hongxing Chen, Changchang Xi
We establish formulas for computation of the higher algebraic -groups of the endomorphism rings of objects linked by a morphism in an additive category. Let be an…
Ringel modules and homological subcategories
Hongxing Chen, Changchang Xi
Given a good -tilting module over a ring , let be the endomorphism ring of , it is an open question whether the kernel of the left-derived functor …
Recollements of derived categories I: Exact contexts
Hongxing Chen, Changchang Xi
Recollements were introduced originally by Beilinson, Bernstein and Deligne to study the derived categories of perverse sheaves, and nowadays become very powerful in understanding…
Stratifications of derived categories from tilting modules over tame hereditary algebras
Hongxing Chen, Changchang Xi
In this paper, we consider the endomorphism algebras of infinitely generated tilting modules of the form over tame hereditary -algebras $…
Good tilting modules and recollements of derived module categories
Hongxing Chen, Changchang Xi
Let be an infinitely generated tilting module of projective dimension at most one over an arbitrary associative ring , and let be the endomorphism ring of . In this p…
Inductions and restrictions for stable equivalences of Morita type
Hongxing Chen, Shengyong Pan, Changchang Xi
In this paper, we present two methods, induction and restriction procedures, to construct new stable equivalences of Morita type. Suppose that a stable equivalence of Morita type b…