The Igusa-Todorov distances of an Artin algebra give a reasonable way of measuring how
far an algebra is from being Igusa-Todorov algebras. We show that the Igusa-Todorov …

We introduce the notion of Igusa-Todorov dimension, and prove that this dimension is an
invariant under derived equivalent. Igusa-Todorov dimension also give a characterization of …

We investigate the inequality $\operatorname {Findim}\Lambda^{op}\leq\operatorname
{dell}\Lambda $ between the finitistic dimension and the delooping level of an Artin algebra …

These notes are devoted to a single invariant, the Gabriel-Roiter measure of finite length
modules: this invariant was introduced by Gabriel (under the name 'Roiter measure') in 1972 …

We give an upper bound for the dimension of the bounded derived categories of (m, n)-
Igusa-Todorov algebras, where m, n are two nonnegative integers. As an applications, we …

In this paper, our primary focus is on investigating the extension dimensions of syzygy
module categories associated with Artin algebras, particularly under various equivalences …

For the module category of an Artin algebra, we generalize the notion of torsion pairs to
ideal torsion pairs. Instead of full subcategories of modules, ideals of morphisms of the …

Co-Gorenstein algebras were introduced by A. Beligiannis in\cite {B}. In\cite {KM}, the
authors propose the following conjecture (Co-GC): if $\Omega^ n (\mod A) $ is extension …

Using a relative version of Auslander's formula, we show that bounded derived category of
every artin algebra admits a categorical resolution. This, in particular, implies that bounded …

We introduce syzygies for derived categories and study their properties. Using these, we
prove the derived invariance of the following classes of artin algebras:(1) syzygy-finite …