place as extension of homomorphism

Theorem.

If $f$ is a ring homomorphism from a subring $𝔬$ of a field $k$ to an algebraically closed field $F$ such that  $f(1)=1$,  then there exists a place (http://planetmath.org/PlaceOfField)

$$\phi :k\to F\cup \{\mathrm{\infty }\}$$

of the field $k$ such that

$${\phi |}_{𝔬}=f.$$

Note.  That $F$ should be algebraically closed, does not , since every field is extendable to such one.