… For non-commutative finite dimensional algebras the question is open, and we prove that if
injectives generate for such an algebra, then the finitistic dimension conjecture holds for that …

… approach to the finitistic dimension conjecture, we propose to … We prove that the Finitistic
Dimension Conjecture holds for the … cases of three) modules of infinite projective dimension. …

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

… A thorough overview of the state of the finitistic global dimension conjecture can be found in
[… prove the finitistic dimension conjecture for algebras with weak representation dimension at …

… finitistic dimension conjecture. In this way we obtain a large class of algebras for which the
finitistic dimension conjecture … finite finitistic dimension for j⩾3, then the finitistic dimension of …

… control the finitistic dimension of eAe. Such a consideration is of particular interest for
understanding the finitistic dimension conjecture. Let us denote the finitistic dimension and global …

… of the finitistic dimension conjecture in terms of extensions and relative global dimensions. …
algebras over a perfect field, this statement is equivalent to the finitistic dimension conjecture, …

… In the sequel, the finitistic dimension conjectures were related to a variety of other … show
that the little finitistic dimension can be strictly larger than the cyclic finitistic dimension and, in fact…

In this note, we prove that if $\Lambda $ is an Artin algebra with a simple module $ S $ of
finite projective dimension, then the finiteness of the finitistic dimension of $\Lambda $ implies …

… After some brief remarks on the origins of homological algebra, we will present the Finitistic
Dimension Conjectures publicized by Bass in 1960, as well as their connections with other …