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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 $\mathfrak{m}$.

See N. Sankharan, A Theorem on Henselian Rings, Canad. Math. Bull. 11 275-277 (1968), 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 The Proposition above is no longer valid if one takes the polynomial ring instead of the power series ring.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.

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 $\mathfrak{m}$.

A reference is the paper by N. Sankharan A Theorem on Henselian Rings, 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 The Proposition above is no longer valid if one takes the polynomial ring instead of the power series ring.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.

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 $\mathfrak{m}$.

See N. Sankharan, A Theorem on Henselian Rings, Canad. Math. Bull. 11 275-277 (1968), in particular Corollary 2.

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 $\mathfrak{m}$.

See N. Sankharan, A Theorem on Henselian Rings, Canad. Math. Bull. 11 275-277 (1968), 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 The Proposition above is no longer valid if one takes the polynomial ring instead of the power series ring.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.

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 $\mathfrak{m}$.

See N. Sankharan, A theorem on Henselian Rings, Canad. Math. Bull. 11 275-277 (1968), in particular Corollary 2.

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 $\mathfrak{m}$.

See N. Sankharan, A Theorem on Henselian Rings, Canad. Math. Bull. 11 275-277 (1968), in particular Corollary 2.