Let be a field extension of a field. Two elements
of are algebraically dependent if there exists a non-zero polynomial such that
. If no such polynomial exists, and are said to be algebraically independent.
More generally, elements
are said to be algebraically dependent if there exists a non-zero polynomial
such that
. If no such polynomial exists, the collection of 's are said to be algebraically independent.
![$ f(x,y)\in K[x,y]$](http://images.planetmath.org:8080/cache/objects/4741/l2h/img5.png "$ f(x,y)\in K[x,y]$"){kind=small}
![$ f(x_1,\ldots,x_n)\in K[x_1,\ldots,x_n]$](http://images.planetmath.org:8080/cache/objects/4741/l2h/img10.png "$ f(x_1,\ldots,x_n)\in K[x_1,\ldots,x_n]$"){kind=small}
