# On $A$ algebra homomorphisms $A[[X_1,…,X_n]]\to Q(A)$, where $A$ is a complete DVR

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 $$\phi(X_i) \in \mathfrak m, \forall i=1,...,n$$ ?