Definition:Affine Algebraic Variety

Definition
An affine algebraic variety is any set which is the intersection of the zero sets of polynomials.

More formally, let $F$ be any field.

Then a subset $S \in F^n$ is an affine algebraic variety if and only if there exists a set of polynomials:
 * $f_i: F^n \to F$

where $i \in I$ is any index set such that:
 * $\displaystyle S = \bigcap_{i \in I} \left\{{x \in F^n : f_i \left({x}\right) = 0 \in Y}\right\}$