# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Laura algebras and quasi-directed components

### Tom 105 / 2006

Colloquium Mathematicum 105 (2006), 179-196 MSC: 16G70, 16G10, 18G05, 16E10. DOI: 10.4064/cm105-2-2

#### Streszczenie

Using a notion of distance between indecomposable modules we deduce new characterizations of laura algebras and quasi-directed Auslander-Reiten components. Afterwards, we investigate the infinite radical of Artin algebras and show that there exist infinitely many non-directing modules between two indecomposable modules $X$ and $Y$ if $\mathop{\rm rad}_{A}^{\infty}(X,Y)\neq 0$. We draw as inference that a convex component is quasi-directed if and only if it is almost directed.

#### Autorzy

• Marcelo LanzilottaCentro de Matemática (CMAT), Iguá 4225
CP 11400, Montevideo, Uruguay
e-mail
• David SmithDépartement de Mathématiques
Université de Sherbrooke
2500, boul. de l'Université