On cyclic vertices in valued translation quivers
Volume 105 / 2006
Colloquium Mathematicum 105 (2006), 45-50
MSC: 16G20, 16G70.
DOI: 10.4064/cm105-1-5
Abstract
Let $x$ and $y$ be two vertices lying on an oriented cycle in a connected valued translation quiver $(\Gamma , \tau , \delta )$. We prove that, under certain conditions, $x$ and $y$ belong to the same cyclic component of $(\Gamma , \tau , \delta )$ if and only if there is an oriented cycle in $(\Gamma , \tau , \delta )$ passing through $x$ and $y$.
