We study the global dimensions of the coherent functors over two categories that are linked
by a pair of adjoint functors. This idea is then exploited to compare the representation …

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 …

For an abelian category A, we establish the relation between its derived and extension
dimensions. Then for an artin algebra Λ, we give the upper bounds of the extension …

The importance of the representation finite Artin algebras for the whole representation theory
of Artin algebras is well understood and there is much literature on the subject (see [1, 6 …

FINITENESS OF REPRESENTATION DIMENSION M. Auslander introduced a concept of
representation dimension of artin algebras in [A], w Page 1 PROCEEDINGS OF THE …

arXiv:0909.0330v1 [math.RT] 2 Sep 2009 Derived dimensions of representation-finite algebras
Page 1 arXiv:0909.0330v1 [math.RT] 2 Sep 2009 Derived dimensions of representation-finite …

We show that the representation dimension of the following classes of algebras is at most
3:(a) Artin algebras A such that the functor HomA (D (A),−) has finite length (or dually, HomA …

Auslander has shown that an algebra is of finite representation type, that is, it admits only
finitely many indecomposable modules up to isomorphism, if and only if its representation …

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

The extension dimensions of an Artin algebra give a reasonable way of measuring how far
an algebra is from being representation-finite. In this paper we mainly study the behavior of …