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 complete1.
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