Abstract algebra | Matroid theory

Algebraic independence

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 . (Wikipedia).

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Transcendental number | If and only if | Indeterminate (variable) | Transcendence degree | Vámos matroid | Zorn's lemma | Algebraic number | Linear independence | Polynomial | Rational number | E (mathematical constant) | Matroid | Field extension | Lindemann–Weierstrass theorem | Gamma function | Field (mathematics) | Real number | Subset | Matroid representation | Abstract algebra | Cardinality | Matrix (mathematics)