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Let $(A,\mathfrak m)$ be a complete Discrete Valuation Ring (complete w.r.t. the $\mathfrak m $-adic topology) with fraction field $K$. Let $\phi : A[[X_1,...,X_n]]\to K$ be an $A$-algebra homomorphism.

Then is it true that $\phi(X_i) \in \mathfrak m, \forall i=1,...,n$ ?

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