We give easy proofs for some well known facts by using some basic property of cleanness. We show that if
(R, m)
is a Noetherian local ring and

is a finitely generated almost clean

-module with the property that

is Cohen-Macaulay for all
P ∈ Ass(M), then depth(M)=min{dim(R/P) : p ∈ Ass(M)}. Using this fact we show that if

is a finitely generated clean

-module such that

is Cohen-Macaulay and

for all minimal prime ideals of

, then

is Cohen-Macaulay. This implies the well known fact that a pure shellable simplicial complex is Cohen-Macaulay.