Pro-p ring
= 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.