A hint to an exercise in my textbook says "Since $B/F$ is finite, it is algebraic, and there are elements $α_1,...,α_n$ with $B=F(α_1,...,α_n)$."
I understand that if $B/F$ is a finite extension then $B$ is algebraic. But why does $B$ being algebraic imply that $B=F(α_1,...,α_n)$?
Thanks in advance!