= Adic topology
{title2=$I^n$}
For a two-sided <ideal> $I$ of a <ring> $R$, the powers $I^n$ form a neighborhood base at zero for the adic topology. For an $R$-<module> $M$, use $I^nM$ on the left or $MI^n$ on the right. Convergence means that for every $n$ the differences eventually belong to the corresponding submodule. The <formal power series ring> $k[[t]]$ and <formal power series module> $M[[t]]$ are complete for $I=(t)$; convergence fixes each finite list of coefficients eventually. This is formal convergence, without an analytic condition on the size of coefficients.
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