1. ## Sum and Intersection

I have the ring Z and two ideals I and J of Z. I need to find for every two ideals of the ring Z their sum and intersection.

What exactly does this mean? Can someone show me a possible solution?

2. Originally Posted by KevinKH
I have the ring Z and two ideals I and J of Z. I need to find for every two ideals of the ring Z their sum and intersection.

What exactly does this mean? Can someone show me a possible solution?
The intersection of $I,J$ is $I\cap J$ another ideal of $\mathbb{Z}$. (Remember they are sets).

I never heard anything about being able to "add" two ideals together. Unless you want to find,
$\{i+j|i\in I \mbox{ and }j\in J\}$.
That is not necessarily an ideal because it not necessarily has the form,
$n\mathbb{Z}$.

3. What do you think I should write as a solution for that question? It seems to just ask for the definition, but it was given in a problem above. Any suggestions?

4. Originally Posted by KevinKH
What do you think I should write as a solution for that question? It seems to just ask for the definition, but it was given in a problem above. Any suggestions?
Are you saying yout book in the problems section asks you to define a natural meaning for "sum of two ideal"? If so then use what I said above, the set formed from all possible additions of the elements.