Definition 1

A ring $C$ is said to be a $p$-ring if the ideal $pC$ of $C$ is maximal, and if $C$ is separated and complete for the $pC$-adic topology.

Let $C$ be a ring; if $p1_C$ is nilpotent and if the ideal $pC$ of $C$ is maximal, $C$ is a $p$-ring, for the $pC$-adic topology of $C$ is discrete. In particular, every field of characteristic $p$ is a $p$-ring.