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 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 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 …

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 …

Let A be an artin algebra, Gélinas has introduced an interesting upper bound for the finitistic
dimension fin-pro A of A, namely the delooping level del A. We assert that fin-pro A= del A …

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 …

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 …

There exists a hierachy of homological conjectures for finitely generated modules over an
Artin algebra A. The generalized Nakayama conjecture for example states that each …

ALGEBRAS OF FINITE SELF-INJECTIVE DIMENSION Page 1 PROCEEDINGS of the
AMERICAN MATHEMATICAL SOCIETY Volume 112, Number 3, July 1991 ALGEBRAS OF …

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 …