I need help with the following proof:

Show that if $\displaystyle \theta$:Z$\displaystyle \rightarrow$Zis a ring isomorphism, then $\displaystyle \theta$ must be the identity mapping. Is there an additive group isomorphism $\displaystyle \theta$:Z$\displaystyle \rightarrow$Zother than the identity mapping?

Thanks

and how do you Z that represents the set of integers in Latex.