How to prove the following conclusion :
For any finite quiver $Q$, an ideal $I$ of $KQ$, contained in $R^2_Q$, is admissible if and only if, for each cycle $\sigma$ in $Q$, there exists $s \geq 1$ such that $ \sigma^s \in I$, where, $R_Q$ is the arrow ideal of the path algebra $KQ$.
This conclusion comes from page 53 of the book named " Elements of the Representation Theory of Associative Algebras Volume1" , but I do not know how to prove it, I need a detailed proof.
For any finite quiver $Q$, a two-sided ideal $I$ of $KQ$ is said to be admissible if there exists $m \geq2$ such that $R^m_Q\subseteq I\subseteq R^2_Q$