  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 $I_{S}=I\cap S$. and $I_{R}=I\cap R$.
