Definition:Zero Locus of Set of Polynomials

Definition
Let $k$ be a field.

Let $A = k \left[{X_1, \ldots, X_n}\right]$ 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


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