Definition:Affine Algebraic Set

Definition
Let $k$ be a field.

Let $A = k[X_1,\ldots,X_n]$ be the ring of polynomial functions in $n$ variables over $k$.

Then a subset $X \subseteq k^n$ is an affine algebraic set if it is the zero locus of some set $T \subseteq A$.

Also see

 * Definition:Zariski Topology on Affine Space
 * Zero Locus of Set is Zero Locus of Generated Ideal