Hello!! I am looking at the following:
Let E/F an extension, S = {α1, . . . , αn} ⊆ E algebraically independent over F
and T ⊇ S a subset of E, that spans E algebraically over F.
Show that there exists a set B between S and T, that is a trancendental basis of E/F, as follows:
Let T\S = {β1, . . . , βm}.
If T = ∅, then B = S is the trancendental basis.
Otherwise, we define S_0 = S and for i = 1, . . . , m,
