We introduce syzygies for derived categories and study their properties. Using these, we
prove the derived invariance of the following classes of artin algebras:(1) syzygy-finite …

Module categories with infinite radical square zero are of finite type Page 1
COMMUNICATIONS IN ALGEBRA, 22(1 I), 451 1-4517 (1994) MODULE CATEGORIES …

We give an alternative proof to the fact that, if the square of the infinite radical of the module
category of an Artin algebra is equal to zero, then the algebra is of finite type by making use …

Given a subbifunctor F of Ext1 (,), one can ask if one can generalize the construction of the
derived category to obtain a relative derived category, where one localizes with respect to F …

Introduction. Let A be an artin algebra and mod A the category of finitely generated (left) A-
modules. In this paper we shall develop sane techniques for constructing almost split …

Let C be an abelian category. Then for any object C in C,~ xt'(C,) is defined as a covariant
functor from C to Ab such that for each X in C EX~'(C, X) is an additive group consisting of …

Let C be a skeletally small abelian category with only a finite number of non-isoaorphic
simple objects and such that each object in C has finite length. Then C has a finite number of …

Lower bounds for the dimension of a triangulated category are provided. These bounds are
applied to stable derived categories of Artin algebras and of commutative complete …

Let Λ be a ℤ-graded artin algebra. It is proved that the category of graded Λ-modules is pure-
semisimple if and only if there are only finitely many nonisomorphic indecomposable finitely …

Recently Sheila Brenner and MCR Butler [7J have studied, the so ca. lled tilting functors,
which are a generalisation of the Berns. tein-Gelfand-Ponomarev reflection functors. Their …