Weak Nullstellensatz

Theorem
Let $K$ be an algebraically closed field.

Let $n \ge 0$ be an natural number.

Let $K \sqbrk {x_1, \ldots, x_n}$ be the polynomial ring in $n$ variables over $k$.

Let $I \subseteq K \sqbrk {x_1,\ldots, x_n}$ be an ideal.


 * 1) $I$ is the unit ideal: $I = (1)$.
 * 2) Its zero-locus is empty set: $\map V I = \O$.