  An extension of $k$-algebras $B \subset A$ is said to have depth one if there
exists a positive integer $n$ such that $ A$ is a direct summand of $ B^n$ in
$_B\mtr{Mod}_B$. Depth one extensions of semisimple algebras are completely
characterized in terms of their centers. For extensions of semisimple Hopf
algebras our results are similar to those obtained for finite group algebra
extensions in \cite{BKone}.
