A finite acyclic graph always contains a sink, a vertex that does not emit edges. Any sink at the graph will generate minimal basic ideal of the Leavitt path algebra over a commutative unital ring. Moreover, the Leavitt path algebra on the finite acyclic graph is a direct sum of minimal basic ideals generated by the sinks. In other words, Leavitt path algebra over the commutative unital ring on the finite acyclic graph is basically semisimple, but not necessarily semisimple. The Leavitt path algebra is semisimple if and only if the commutative unital ring is semisimple.

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