Definition:Affine Algebraic Set

Definition
Let $K$ be a field.

Let $A = K \sqbrk {X_1, \ldots, X_n}$ be the ring of polynomial functions in $n$ variables over $K$.

Then a subset $X \subseteq K^n$ is an affine algebraic set 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
 * Definition:Projective Algebraic Set