Should the terminology "$K$-embedding" be regarded as a homomorphism of $K$ -vector spaces?

Question

Let $L|K$ be a finite field extension. Denote the algebraic closure of $K$ by $\bar K$.

Let $\operatorname {Hom}_K(L,\bar{K})$ denote the set of all $K$ -embeddings of $L$ in $\bar K$.

Should the terminology "$K$-embedding" be regarded as a homomorphism of $K$ -vector spaces?

Answer 1

In the context of field theory, a $K$-embedding is most probably a homomorphism of $K$-algebras, that is, a ring homomorphism that fixes $K$.