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Completion of $K$-algebra of finite type with respect to the residue norm
Let $K$ be a non-archimedean field. For $n \in \mathbb{N}$ let
\begin{equation*}
T_n=\{ \sum_{\nu_1, \ldots, \nu_n \geq 0 } a_{\nu_1, \ldots, \nu_n }X_1^{\nu_1}\cdots X_n^{\nu_n} \in K[\
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