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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,...,α_n of elements of S, no two the same, and every non-zero polynomial P(x₁,...,x_n) with coefficients in K, we have

P(α₁,...,α_n)≠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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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Algebraically independent".