A field extension \(L/k\) is algebraic if every \(\alpha \in L\) is algebraic over \(k\), that is, a root of some nonzero polynomial \(f\in k[x]\).
When is a field extension $L/k$ algebraic?
When is a field extension $L/K$ algebraic?
When is a field extension $L/K$ algebraic over $K$?