Let $K$ be an algebraically closed field. Then let $A = K[x_1, ... , x_n]$.
If $Y \subseteq \mathbb A^n$, then the ideal of $Y$ is to defined to be $I(Y) = \{f \in A | f(P) = 0 \ \forall P \in Y \}$. What is $I(\emptyset)$?
For $T \subseteq A$, define $Z(Y) = \{P \in \mathbb A^n | f(P) = 0 \ \forall f \in A\}$. Am I correct in thinking that $Z(A) = \emptyset$?
Thanks