  In the work we have considered Breuil-Kisin module over the ring of witt
vectors $W(\kappa)$ over the residue field $\kappa$ of characteristic $p$ and a
finite flat $\mathbb{Z}_p$-algebra $R$. Then considered Breuil-Kisin modules
$M$ over the ring $W(\kappa)$ and taking the action of $R$ on $W(\kappa)$, we
get again a Breuil-Kisin module $M$ over the ring $R \otimes_{\mathbb{Z}_p}
W(\kappa)$. We have studied freeness and projectiveness of this module.
