We use the class of representation-finite algebras to investigate the finitistic dimension
conjecture. In this way we obtain a large class of algebras for which the finitistic dimension …

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 …

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 …

Let A be an Artin algebra and e be an idempotent element of A. We prove that if A has
representation dimension at most three, then the finitistic dimension of eAe is finite, and …

The famous finitistic dimension conjecture says that every finite-dimensional 𝕂-algebra over
a field 𝕂 should have finite finitistic dimension. This conjecture is equivalent to the following …

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 …

We find a simple condition which implies finiteness of finitistic global dimension for artin
algebras. As a consequence we obtain a short proof of the finitistic global dimension …

In 2005, the second author and Todorov introduced an upper bound on the finitistic
dimension of an Artin algebra, now known as the ϕ ϕ-dimension. The ϕ ϕ-dimension …

We study Auslander's representation dimension of Artin algebras, which is by definition the
minimal projective dimension of coherent functors on modules which are both generators …

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 …