… radical of mod A and by rad * (mod A) the infinite radical of mod A, that is, the infinite power of
rad (mod A)… Denote by IT, the Auslander–Reiten quiver of A, and by t and t T the Auslander–…

… The Auslander±Reiten quiver yields a description of the category of A-modules modulo
its infinite radical radq A, which is the intersection of the (finite) powers of the radical of mod-A, …

Throughout this paper we assume that all modules are finitely generated over an artin
algebra L!. We denote by mod/i the category of all finitely generated/i-modules. The notions of …

… A) the infinite radical of mod A, and I'A the AuslanderReiten quiver of A. … AuslanderReiten
components. Recall that following [12], [36], a connected component C of the Auslander-Reiten …

… We point out that there is information along the same lines for infinite representation type,
since there are still combinatorial results for additive and subadditive functions [15]. …

… Let A be an artin algebra, mod A the category of finitely generated right .4-modules, rad (mod
A) the infinite radical of mod A, and Γ^ the AuslanderReiten quiver of A. It is known that Γ^ …

… want to describe the radical of a finitely presented C-module M. We define the radical of M, …
If rim ~ 0 for all i, then we say that the Loewy length of M is infinite. Otherwise we define the …

… If C is an additive subcategory of X whose radical is right nilpotent, then add(Ind X — IndC)
is covariantly finite in X. In particular if C is an additive category whose radical is right nilpotent…

The aim of this paper is to present a method for finding presentations of Grothencheck groups
of abelian categories. This method depends on the concept of a coherent pair (A, B) of …

… infinite number of nonisomorphic indecomposable CM modules M= MO LI M, + ... generated
by their degree zero component, R is of infinite … Let /i be an artin algebra with radical r, such …