Elements 
of a field extension 
are algebraically dependent over 
if there is a nonzero polynomial ![F in K[X_1,...,X_n]](/images/equations/AlgebraicallyDependent/Inline4.svg)
such that 
.
Otherwise they are algebraically independent
over 
.
Algebraically Dependent
See also
Algebraic Extension, Algebraically Independent, Transcendence DegreeExplore with Wolfram|Alpha
References
Reid, M. Undergraduate Commutative Algebra. Cambridge, England: Cambridge University Press, 1995.Cite this as:
Weisstein, Eric W. "Algebraically Dependent." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlgebraicallyDependent.html