Wedderburn-Malcev decomposition of one-sided ideals of finite dimensional algebras

Let $A$ be a finite dimensional associative algebra over a perfect field and let $R$ be the radical of $A$. We show that for every one-sided ideal $I$ of $A$ there exists a semisimple subalgebra $S$ of $A$ such that $I=I_{S}\oplus I_{R}$where$I_{S}=I\cap S$\mathrm{.}and$I_{R}=I\cap R$.