Quasivarieties of modules over path algebras of quivers (Q2433104)

Let \(F\Gamma\) be a finite-dimensional path algebra of a quiver \(\Gamma\) over a field \(F\). A quiver is a directed multigraph. Let \({\mathbf L}\) and \({\mathbf R}\) denote the varieties of all left and right \(F\Gamma\) modules, respectively. It is proved that the following statements are equivalent: 1. The subvariety lattice of \({\mathbf L}\) is a sublattice of the subquasivariety lattice of \({\mathbf L}\). 2. The subquasivariety lattice of \({\mathbf R}\) is distributive. 3. \(\Gamma\) is an ordered forest.