Laura algebras and quasi-directed components
Volume 105 / 2006
Colloquium Mathematicum 105 (2006), 179-196
MSC: 16G70, 16G10, 18G05, 16E10.
DOI: 10.4064/cm105-2-2
Abstract
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.
