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

An element $f \in A$ is called

*topologically nilpotent*if $f^ n \to 0$ as $n \to \infty $.A

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

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

*weakly admissible*if $A$ is weakly pre-admissible and complete^{1}.

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