Suppose $k$ is a field and let $n > m$. Does there exist injective homomorphisms $$ k [[x_1, x_2, \ldots, x_n]] \rightarrow k[[x_1, x_2, \ldots, x_m]]\ ?$$
Injective map between power series ring
8
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abstract-algebra
commutative-algebra
power-series
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1no, it is from the "false beliefs" thread at MO. – 2011-09-30
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3Taken from http://mathoverflow.net/a/25231 – 2015-07-08