1.Adjective(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
{
α
}
{\displaystyle \{\alpha \}}
is algebraically independent over
K
{\displaystyle K}
if and only if the element
α
{\displaystyle \alpha }
is transcendental over
K
{\displaystyle K}
.; A subset
S
⊂
L
{\displaystyle S\subset L}
is algebraically independent over
K
{\displaystyle K}
if every element of
S
{\displaystyle S}
is transcendental over
K
{\displaystyle K}
and over each of the extension fields over
K
{\displaystyle K}
generated by the remaining elements of
S
{\displaystyle S}
."