Affine algebraic variety

Definition
An affine algebraic variety (or simply an affine variety) is an irreducible closed subset of the affine space over a field (when equipped with the Zariski topology).

In other words, it is the set of points in affine space that are the solution to an ideal of polynomials in the polynomial ring, where this ideal cannot be expressed as the product of two ideals properly containing it.

Related notions

 * Projective algebraic variety
 * Quasi-affine algebraic variety
 * Quasi-projective algebraic variety
 * Algebraic variety