… 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, …

… of a domestic algebra whose module category does not have its infinite radical nilpotent.
Recall that … , and the nilpotency of the infinite radical of its module category are equivalent. It Ž …

… First we define a K-module structure for an arbitrary faithful A-module F of type 3. Given y
GF with 7*0, then -yA = F and so given any y' E F there exists a'G A with y' = y • a'. Now, for any …

… A nyright V -module B becomes a right U-module if the action of the operators is dened
as follows: a± u = a( u'), we will say that the module B is converted into the U-module B' by …

… We have defined an additive category 3t induced from a family of completely indecomposable
… denote the Jacobson radical of S and by $ M we denote $ Π EndR(M) for an i?-module M. …

… We are now in a position to define the radical of an additive category %. We embed ^ in a
direct category 2 as in § 2, and we take the unique ideal 8% of 3i such that &P is the radical of £…

… By an A-module is meant a finite dimensional right A-module. We shall denote by mod A
the category of finite- dimensional right A-modules, by rad(mod A) the radical of mod A, and by …

… describe the relation of a module that satisfies a weakly versions of the radical formulae and
its … of the radical formula, we define a fully primal module and a fully weakly primal module. …

… τ a hereditary torsion theory on the category σ[M] we use the concept of prime and semiprime
module defined by Raggi et al. to introduce the concept of τ-pure prime radical Nτ (M) = Nτ …

… We denote by J(R) the Jacobson radical of R. We recall that … We denote by modR the category
of finitely generated right fi-… Following [11] by the Jacobson radical of the category modR …