= Complete discrete valuation ring
{title2=$R\simeq\varprojlim_n R/\mathfrak m^n$}
A complete discrete <valuation> ring is a <discrete valuation ring> complete for its maximal-ideal-adic topology. Equivalently, the canonical map to the <inverse limit> of the residue rings is an isomorphism: compatible residue classes determine a Cauchy sequence, and completeness gives its unique limit. Standard examples are $\mathbb Z_p$ and $k[[t]]$. This completeness is the hypothesis that makes <Newton iteration over a valued field> converge in the ring in the usual <Hensel lemma>.
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