Almost all derivative quivers of artinian biserial rings contain chains

Abstract

A lower estimate for the number \(M_n\) of all labelled quivers with n–vertex parts of Artinian biserial rings is given and the asymptotic of the relation \(M_n/B_n\), where \(B_n\) denotes the number of those quivers all connected components of which are cycles, is studied.