The Stacks project

[Definition 8.3.8, Gabber-Ramero]

Definition 86.7.1. 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.

[1] In [Gabber-Ramero] the authors say $A$ is $c$-adic.
[2] By our conventions this includes separated.

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