Definition 85.4.8. 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.

There are also:

• 2 comment(s) on Section 85.4: Topological rings and modules

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).