References Page 1 References [1] S. Abhyankar, S. Wiegand, On the compositum of two power
series rings, Proc. Amer. Math. Soc. 112 (1991), 629 – 636. [2] U. Albrecht, Endomorphism …

We define a dimension for a triangulated category. We prove a representability Theorem for
a class of functors on finite dimensional triangulated categories. We study the dimension of …

We introduce the concept of maximal (n− 1)-orthogonal subcategories over Artin algebras
and orders, and develop (n+ 1)-dimensional Auslander–Reiten theory on them. We give the …

We study Auslander correspondence from the viewpoint of higher-dimensional analogue of
Auslander–Reiten theory [O. Iyama, Higher dimensional Auslander–Reiten theory on …

We investigate several homological aspects of recollements of abelian categories. In
particular, we study how various homological invariants and dimensions of the categories …

We determine the representation dimension of exterior algebras. This provides the first
known examples of representation dimension> 3. We deduce that the Loewy length of the …

Radical embeddings and representation dimension Page 1 http://www.elsevier.com/locate/aim
Advances in Mathematics 185 (2004) 159–177 Radical embeddings and representation …

We recall several results in Auslander-Reiten theory for finite-dimensional algebras over
fields and orders over complete local rings. Then we introduce $ n $-cluster tilting …

THE FINITISTIC DIMENSION CONJECTURES - A TALE OF 3.5 DECADES 1. Introduction
Since the last five years have brought fresh initia Page 1 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 …