Definition 86.14.7. Let $A$ be an adic topological ring which has a finitely generated ideal of definition. Let $f \in A$. The *completed principal localization* $A_{\{ f\} }$ of $A$ is the completion of $A_ f = A[1/f]$ of the principal localization of $A$ at $f$ with respect to any ideal of definition of $A$.

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