Abstract
Let $k[[x,y]]$ be the formal power series ring in two variables over a field $k$ of characteristic zero and let $d$ be a nonzero derivation of $k[[x,y]]$. We prove that if $\mathop{\rm Ker}\nolimits (d)\neq k$ then $\mathop{\rm Ker}\nolimits (d) =\mathop{
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