Gorenstein homological algebra is a kind of relative homological algebra which has been
developed to a high level since more than four decades. In this report we review the basic …

Let R be an isolated Gorenstein singularity with a non-commutative resolution A= End R
(R⊕ M). In this paper, we show that the relative singularity category Δ R (A) of A has a …

An artin algebra is called CM-free provided that all its finitely generated Gorenstein
projective modules are projective. We show that a connected artin algebra with radical …

Generalizing Tate's results for tori, we give closed formulas for the abelian Galois
cohomology groups H^ 1_ {ab}(F, G) and H^ 2_ {ab}(F, G) of a connected reductive group G …

Given an artin algebra $\Lambda $ with an idempotent element $ a $ we compare the
algebras $\Lambda $ and $ a\Lambda a $ with respect to Gorensteinness, singularity …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

Stable equivalences of Morita type preserve many interesting properties and are proved to
be the appropriate concept for studying equivalences between stable categories. Recently …

Abstract Let T=(RM 0 S) be a triangular matrix ring with R and S rings and RMS an R–S-
bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result …

For a Frobenius abelian category $\mathcal {A} $, we show that the category ${\rm
Mon}(\mathcal {A}) $ of monomorphisms in $\mathcal {A} $ is a Frobenius exact category; …

We study the relationship between singularity categories and relative singularity categories
and discuss constructions of differential graded algebras of relative singularity categories …