We solve a long standing open problem concerning the structure of finite cycles in the
category mod A of finitely generated modules over an arbitrary artin algebra A, that is, the …

For Artin algebras allowing certain filtered module categories, the Generalized Nakayama
Conjecture is shown to be true; our result covers all positively graded Artin algebras and …

Let $\Lambda $ and $\Gamma $ be Artin algebras, $ M $ a $\Gamma-\Lambda $-bimodule,
and $ R $ the triangular matrix ring of $\Lambda,\Gamma $, and $ M $; assume that $ R $ is …

Throughout this paper A denotes an artin algebra over a commutative artin ring R; ie, A is an
R-algebra which is finitely generated as an R-module. All A-modules are assumed to …

We consider artin algebras with duality functor D. We consider left modules (usually, we call
them just modules) as well as right modules. Maps will act on the opposite side of the …

Let modA be the category of finitely generated right A-modules over an artin algebra⋀, and F
be an additive subfunctor of. Let P (F) denote the full sucategory of A with objects the F …

INTRODUCTION. An artin algebra is an Artin ring which is a finitely generated module over
its center R, which is also an Artin ring. For an Artin algebra A we denote by mod (A) the …

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 …

If $\Lambda $ is an artin algebra there is a partition of $\operatorname {ind}\Lambda $, the
category of indecomposable finitely generated $\Lambda $-modules, $\operatorname …

For certain abelian categories with radical square zero, containing artin rings with radical
square zero as a special case, we give a way of constructing hereditary abelian categories …