algebraically independent
whose elements do not satisfy any non-trivial polynomial equation with coefficients in K(Of a subset S of the extension field L of a given field extension L / K) whose elements do not satisfy any non-trivial polynomial equation with coefficients in K.
Meaning
1 senses(not comparable)(Of a subset S of the extension field L of a given field extension L / K) whose elements do not satisfy any non-trivial polynomial equation with coefficients in K.
The singleton set #92;#123;#92;alpha#92;#125; is algebraically independent over K if and only if the element #92;alpha is transcendental over K.
A subset S#92;subsetL is algebraically independent over K if every element of S is transcendental over K and over each of the extension fields over K generated by the remaining elements of S.