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 …

In this paper we develop new reduction techniques for testing the finiteness of the finitistic
dimension of a finite dimensional algebra over a field. Viewing the latter algebra as a …

Torsion pairs in recollements of abelian categories Page 1 Front. Math. China 2018, 13(4):
875–892 https://doi.org/10.1007/s11464-018-0712-1 Torsion pairs in recollements of abelian …

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We prove that a certain eventually homological isomorphism between module categories
induces triangle equivalences between their singularity categories, Gorenstein defect …

We exploit singular equivalences between artin algebras that are induced from certain
functors between the stable module categories. Such functors are called pre-triangle …

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 …

A new approach is established to compare Hochschild cohomologies of an algebra and of
its centralizer subalgebras. This approach is based on dominant dimension, a homological …

Given a noncommutative partial resolution A= End R (R⊕ M) of a Gorenstein singularity R,
we show that the relative singularity category Δ R (A) of Kalck–Yang is controlled by a …

The paper is devoted to study some of the questions arises naturally in connection to the
notion of relative derived categories. In particular, we study invariants of recollements …