# Injective map on power series ring

Suppose $k$ is a field and let $n > m$. Does there exist injective homomorphisms of the form:

$$k [[x_1, x_2, \ldots, x_n]] \rightarrow k[[x_1, x_2, \ldots, x_m]]$$

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 What is the second thing? Missed a $k$? – Rasmus Sep 30 '11 at 13:18 @Rasmus: Thanks. – Valeriya Sep 30 '11 at 13:24 What have you tried? Is this a homework question (it reads like one)? – Rasmus Sep 30 '11 at 13:35 no, it is from the "false beliefs" thread at MO. – Valeriya Sep 30 '11 at 13:52