[HTML][HTML] On the finitistic dimension conjecture I: related to representation-finite algebras
C Xi - Journal of pure and applied algebra, 2004 - Elsevier
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 …
conjecture. In this way we obtain a large class of algebras for which the finitistic dimension …
On the finitistic dimension conjecture II: related to finite global dimension
C Xi - Advances in Mathematics, 2006 - Elsevier
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 …
relationship between the global dimensions of the given algebras, on the one hand, and the …
On the finitistic dimension conjecture, III: Related to the pair eAe⊆ A
C Xi - Journal of Algebra, 2008 - Elsevier
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 …
homological conditions on A to control the finitistic dimension of eAe. Such a consideration …
On the finitistic dimension conjecture of Artin algebras
A Zhang, S Zhang - Journal of Algebra, 2008 - Elsevier
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 …
representation dimension at most three, then the finitistic dimension of eAe is finite, and …
The finitistic dimension conjecture and relatively projective modules
C Xi, D Xu - Communications in Contemporary Mathematics, 2013 - World Scientific
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 …
a field 𝕂 should have finite finitistic dimension. This conjecture is equivalent to the following …
Finitistic dimension and Igusa–Todorov algebras
J Wei - Advances in Mathematics, 2009 - Elsevier
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 …
dimension conjecture, and the conjecture is proved for those algebras. Such algebras …
[PDF][PDF] On the finitistic global dimension conjecture for Artin 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 …
algebras. As a consequence we obtain a short proof of the finitistic global dimension …
Representation dimension and quasi-hereditary algebras
C Xi - Advances in Mathematics, 2002 - Elsevier
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 …
minimal projective dimension of coherent functors on modules which are both generators …
An approach to the finitistic dimension conjecture
F Huard, M Lanzilotta, O Mendoza - Journal of algebra, 2008 - Elsevier
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 …
category of all finitely generated left R-modules. For a given full subcategory X of modR, we …