The Stacks project

Definition 87.7.1. Let $A$ be a linearly topologized ring.

1. We say $A$ is weakly pre-adic¹ if there exists an ideal $I \subset A$ such that the closure of $I^ n$ is open for all $n \geq 0$ and these closures form a fundamental system of open ideals.

2. We say $A$ is weakly adic if $A$ is weakly pre-adic and complete².