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Antoine Ducros
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About the Ddmension of a complete local ring

Let k be a field, and let A be a local, noetherian, complete k-algebra with residue field k. Suppose that there are elements t_1,....t_n in the maximal ideal of A such that the map k[[X_1,....X_n]]---->A that sends X_i to t_i for all i is injective. Is the dimension of A greater or equal than n ?

Antoine Ducros
  • 1.6k
  • 10
  • 13