Maysam Mosadeq - Department of Mathematics, Larestan Branch, Islamic Azad University, Larestan, Iran.

Let \varphi:A\to B be an isomorphism of C^*-algebras and I be an ideal of A.  Introducing the concepts of unitary equivalent and the implemented Finsler modules, we show that the \frac{A}{I}-module \frac{E}{E_{I}} and the implemented  \frac{B}{\varphi(I)}-module  \frac{F}{F_{\varphi(I)}}  are unitary equivalent. We also,  establish a one to one correspondence between  the groups U(E) and U(F) of  unitaries on full Finsler modules E and F, respectively.   Finally, we explain regularized  dynamical systems and   apply the aforementioned one to one correspondence to prove that  each regularized  dynamical system in U(E) implements a   regularized  dynamical system  in U(F).

C^*-Dynamical systems‎, ‎generalized derivation‎, ‎Finsler module‎, ‎ternary derivation‎, ‎one parameter group, unitary operator