A subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non-trivial polynomial equation with coefficients in K, that is, if for every finite sequence α1,...,αn of elements of S, no two the same, and every non-zero polynomial P(x1,...,xn) with coefficients in K, we have
- P(α1,...,αn)≠0.