Practice problem

Hom, Tensor and Limits

A coefficient field of a local ring is a field inside of it isomorphic to the residue field.

Let $A$ be a local ring, with maximal ideal $\mathfrak{m}$ and residue field $k = A/\mathfrak{m}$ . What can you say about the set of ring homomorphisms $\operatorname{Hom}(k,A)$ ? Mark all that apply.