Algebraically independent
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.
In particular, a one element set {α} is algebraically independent over K if and only if α is transcendental over K.
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