Algebraic independence
In abstract algebra, a subset S {\displaystyle S} of a field L {\displaystyle L} is algebraically independent over a subfield K {\displaystyle K} if the elements of S {\displaystyle S} do not satisfy any non-trivial polynomial equation with coefficients in K {\displaystyle K} . In particular, a one element set { α } {\displaystyle \{\alpha \}} is algebraically independent over K {\displaystyle K} if and only if α {\displaystyle \alpha } is transcendental over K {\displaystyle K} .