The Stacks project

Definition 87.4.8. Let $A$ be a linearly topologized ring.

  1. An element $f \in A$ is called topologically nilpotent if $f^ n \to 0$ as $n \to \infty $.

  2. A weak ideal of definition for $A$ is an open ideal $I \subset A$ consisting entirely of topologically nilpotent elements.

  3. We say $A$ is weakly pre-admissible if $A$ has a weak ideal of definition.

  4. We say $A$ is weakly admissible if $A$ is weakly pre-admissible and complete1.

[1] By our conventions this includes separated.

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