  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 \"{U}lger into $n-th$
dual of Banach $A-modules$ where $n\geq 0$ is even number. 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 group
algebras.
