Steinitz field towers for modular fields
Saunders MacLane · Transactions of the American Mathematical Society · 1939
A set of elements is algebraically independent over a field if the elements satisfy no non-trivial polynomial equations with coefficients in the field.f Here T-\x\ denotes the set T with the element x deleted.* F. K. Schmidt [2] states without proof a similar theorem, omitting the property, essential to our purposes, that L is relatively algebraically closed in K.t L is relatively algebraically closed in K if and only if every element of K algebraic over L is in L.