This is the first of a two-volume set that provides a modern account of the representation
theory of finite dimensional associative algebras over an algebraically closed field. The …

In this paper, we study the finitistic dimensions of artin algebras by establishing a
relationship between the global dimensions of the given algebras, on the one hand, and the …

The notion of Igusa–Todorov algebras is introduced in connection with the (little) finitistic
dimension conjecture, and the conjecture is proved for those algebras. Such algebras …

Let A be an Artin algebra and e an idempotent element in A. In this paper, we use co-
homological conditions on A to control the finitistic dimension of eAe. Such a consideration …

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 …

We will study the resolution dimension of functorially finite subcategories. The subcategories
with the resolution dimension zero correspond to ring epimorphisms, and rejective …

Let AA be an abelian category having enough projective objects and enough injective
objects. We prove that if AA admits an additive generating object, then the extension …

Let R be a finite dimensional k-algebra over an algebraically closed field k and modR be the
category of all finitely generated left R-modules. For a given full subcategory X of modR, we …

In this article, we prove that, under certain conditions, Morita context algebras that arise from
Igusa-Todorov (LIT) algebras and have zero bimodule morphisms are also Igusa-Todorov …

We consider a class of extensions of both abstract and pseudocompact algebras, which we
refer to as" strongly proj-bounded extensions". We prove that the finiteness of the left global …