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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

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