Algebraic independence
Set without nontrivial polynomial equalities / From Wikipedia, the free encyclopedia
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In abstract algebra, a subset of a field is algebraically independent over a subfield if the elements of do not satisfy any non-trivial polynomial equation with coefficients in .
In particular, a one element set is algebraically independent over if and only if is transcendental over . In general, all the elements of an algebraically independent set over are by necessity transcendental over , and over all of the field extensions over generated by the remaining elements of .