Tracial cyclic Rokhlin property for automorphisms on simple

  not necessarily unital C*-algebras is investigated.

   We show that if $A$ is a simple (not necessarily unital) C*-algebra with property $(T_{0})$,

   $alphainmathrm{Aut(A)}$ is an automorphism with  tracial cyclic Rokhlin property,

   then $A rtimes _{alpha}mathbb{Z}$ is simple with property $(T_{0})$.

  We also show that the performance automorphisms is preserved by going to certain subalgebras and taking direct limit or tensor product.