Sum and Intersection

**KevinKH** · October 26th 2006, 09:49 AM

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?

**ThePerfectHacker** · October 26th 2006, 09:57 AM

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,
$n\mathbb{Z}$ .

**KevinKH** · October 26th 2006, 10:06 AM

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?

**ThePerfectHacker** · October 26th 2006, 10:11 AM

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.

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