affine variety

In algebraic geometry, an affine variety over an algebraically closed field k is the zero-locus in the affine n-space  of some finite family of polynomials of n variables with coefficients in k that generate a prime ideal. If the condition of generating a prime ideal is removed, such a set is called an (affine) algebraic set. A Zariski open subvariety of an affine variety is called a quasi-affine variety.