Abstract:
Let K be a field, Q = (Q0, Q1) be a quiver and KQ be the generalised path algebra
[10]. This paper gives a characterisation for the right and left modules over the path algebras of
finite acyclic quiver. The study shows that the modules over such path algebras could be written
as the decomposition of KQ-submodules. For KQ-modules over path algebras of quiver with
countably many vertices, a sequence of KQ-submodules is identified which in finite case is a
composition series.
