Idempotent Generated Endomorphisms of an Independence Algebra
  The aim of this note is to give a direct proof for the following result proved by Fountain and Lewin: {\em Let $\alg$ be an independence algebra of finite rank and let $a$ be a singular endomorphism of $\alg $. Then $a=e_1... e_n$ where $e^2_i=e_i$ and $rank(a)=rank(e_i)$.} 
Jo\~ao Ara\'ujo
math.GR