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Suppose $k$ is a field and let $n > m$. Does there exist injective homomorphisms $$ k [[x_1, x_2, \ldots, x_n]] \rightarrow k[[x_1, x_2, \ldots, x_m]]\ ?$$

  • 1
    no, it is from the "false beliefs" thread at MO.2011-09-30
  • 3
    Taken from http://mathoverflow.net/a/252312015-07-08

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