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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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