# Thread: Ideals of Algebraic Sets

1. ## Ideals of Algebraic Sets

Hello, I was wondering if someone could give me a hint about where to start with the following problem. Any help would be appreciated.

(definitions)
Let $\displaystyle k$ be an algebraically closed field. Then let $\displaystyle J,J' \subseteq k[x_1,\ldots,x_n]$ be ideals. Then let $\displaystyle X = V(J), X' = V(J')$, i.e. algebraic sets. The ideal of $\displaystyle X$is $\displaystyle I_X := \{ f \in k[x_1 ,\ldots, x_n] | f(x) = 0 \forall x \in X\}$.

(problem)
give an example to show that $\displaystyle I_{X \cap X'} \not= I_X + I_{X'}$

2. ## Re: Ideals of Algebraic Sets

Originally Posted by slevvio
Hello, I was wondering if someone could give me a hint about where to start with the following problem. Any help would be appreciated.

(definitions)
Let $\displaystyle k$ be an algebraically closed field. Then let $\displaystyle J,J' \subseteq k[x_1,\ldots,x_n]$ be ideals. Then let $\displaystyle X = V(J), X' = V(J')$, i.e. algebraic sets. The ideal of $\displaystyle X$is $\displaystyle I_X := \{ f \in k[x_1 ,\ldots, x_n] | f(x) = 0 \forall x \in X\}$.

(problem)
give an example to show that $\displaystyle I_{X \cap X'} \not= I_X + I_{X'}$
this is just the geometric version of this question, that i've already answered.