algebraically independent

Adjective

Meaning

algebraically independent (not comparable)

(algebra, field theory) (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}

.

Antonyms

Close letter words and terms