= Canonical Coleman decomposition of power-series units
{title2=$R^\times\simeq W\times(1+pR)$}
Let $W$ be the <subgroup> fixed by the <Coleman norm operator>. The <Coleman norm-fixed lift> gives the unique factorization $f=w(\overline f)v$, with $v\in1+pR$. Multiplication consequently gives the displayed <direct product of groups>, while reduction identifies $W$ with $\mathbb F_p[[T]]^\times$. This is a decomposition of <unit groups>, not an identification of a power-series <ring> with a product of groups.
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