Example

Let C be a $p$-ring. The ring of formal series $A = C[[T_1, ..., T_n]]$ is a noetherian, local, separated and complete ring, whose maximal ideal is generated by the sequence $(p, T_1, ..., T_n)$. It is immediate that C is a Cohen subring of A. This applies in particular when C is equal to $\mathbf{Z}_p$, to $\mathbf{Z}/p^n \mathbf{Z}$ or to a field of characteristic $p$.