  In this paper, we will study the topological centers of $n-th$ dual of Banach
$A-module$ and we extend some propositions from Lau and $\ddot{U}lger$ into
$n-th$ dual of Banach $A-modules$. Let $B$ be a Banach $A-bimodule$. By using
some new conditions, we show that ${{Z}^\ell}_{A^{(n)}}(B^{(n)})=B^{(n)}$ and
${{Z}^\ell}_{B^{(n)}}(A^{(n)})=A^{(n)}$. We also have some conclusions in dual
groups.
