A Note on the Radical of a Module Category |
| |
Authors: | Claudia Chaio |
| |
Affiliation: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales , Universidad Nacional de Mar del Plata , Argentina |
| |
Abstract: | We characterize the finiteness of the representation type of an artin algebra in terms of the behavior of the projective covers and the injective envelopes of the simple modules with respect to the infinite radical of the module category. In case the algebra is representation-finite, we show that the nilpotency of the radical of the module category is the maximal depth of the composites of these maps, which is independent from the maximal length of the indecomposable modules. |
| |
Keywords: | Artin algebras Depth of a morphism Finite representation type Harada-Sai Lemma Injective envelope Projective cover Radical of a module category |
|
|