Let $R$ be a henselian ring. Is $R[[x]]$ also a henselian ring?



Formal power series over a henselian ring
Yes, it is. 
More generally, the following result holds.



> 
> **Proposition.** If $R$ is henselian at the maximal ideal $\mathfrak{m}$, then $R[[x\_1, \ldots, x\_n]]$ is henselian at the maximal ideal lying over $\mathfrak{m}$.
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A reference is the paper by N. Sankharan [*A Theorem on Henselian Rings*](http://cms.math.ca/10.4153/CMB-1968-032-4), Canad. Math. Bull. **11** (1968), 275-277. See in particular Corollary 2.


**Remark.** The Proposition above is no longer valid if one takes the polynomial ring instead of the power series ring. For instance, if $K$ is a field than $K$ is henselian but $K[x]$ is not. 


