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 $\text{alg}$ be an independence algebra of finite rank and let $a$ be a singular endomorphism of $\text{alg}$. Then $a=e_1… e_n$where$e^2_i=e_i$and$rank(a)=rank(e_i)$.}