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 part of …

We introduce a generalization of tilting modules of finite projective dimension, projectively
Wakamatsu tilting modules, which are self-orthogonal and Ext-progenerators in their Ext …

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

We study the homotopy category of unbounded complexes of Gorenstein-projective
modules with bounded relative homologies. We show the existence of a right recollement of …

Let $\Lambda $ be an arbitrary monomial algebra. We investigate the stable category
$\underline {\operatorname {Gproj}}^{\mathbb {Z}}\Lambda $ of graded Gorenstein …

Using the Morita-type embedding, we show that any exact category with enough projectives
has a realization as a (pre) resolving subcategory of a module category. When the exact …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …

For self-injective algebras, Rickard proved that each derived equivalence induces a stable
equivalence of Morita type. For general algebras, it is unknown when a derived equivalence …

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

In this paper we show that how the representation theory of subcategories (of the category of
modules over an Artin algebra) can be connected to the representation theory of all modules …