Definition:Affine Algebraic Variety

Definition
Let $k$ be a field.

Let $n \ge 1$ be an Integer.

Then a subset $X \subseteq k^n$ is an affine algebraic variety if the following hold:


 * $(1): \quad X$ is an affine algebraic set


 * $(2): \quad X$ is irreducible the Zariski topology.

Also see

 * Definition:Affine Scheme