Definition:Zero Locus of Set of Polynomials

Definition
Let $k$ be a field.

Let $A = k[X_1,\ldots,X_n]$ be the Ring of Polynomial Functions in $n$ variables over $k$.

Let $T \subseteq A$ be a set.

Then the zero locus of $T$ is the set


 * $V(T) = \{ x \in k^n : f(x) = 0,\ \forall f \in T \}$