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On cyclic vertices in valued translation quivers

Volume 105 / 2006

Piotr Malicki 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 $y$.

Authors

  • Piotr MalickiFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail

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