Pro-p ring

A pro-$p$ ring is a topological ring with continuous ring operations whose underlying additive group is a pro-p group. Standard local analytic examples are complete Noetherian local rings with finite residue field of characteristic $p$, such as ${\mathbb{Z}}_p$ and ${\mathbb{F}}_p[[t]]$. The topology is essential to the convergence of power series used for analytic group operations.