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

Abstract

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 $I_R=I\cap R$.

Communications in Algebra (to appear)