If A and B are both ideals, then A+B is an ideal. How can you show this?

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- Jan 19th 2010, 10:07 AMRyaηSum of Ideals
If A and B are both ideals, then A+B is an ideal. How can you show this?

- Jan 19th 2010, 10:09 AMSwlabr
- Jan 19th 2010, 10:27 AMRyaη
Is it anything like this?

For some ring R that has A and B as ideals.

$\displaystyle nA \in R$ and $\displaystyle nB \in R$, then $\displaystyle nA+nB \in R$. Thus, $\displaystyle n(A+B) \in R$. Therefore $\displaystyle (A+B) \in R$. - Jan 19th 2010, 10:43 AMSwlabr
- Jan 20th 2010, 06:08 PMRyaη
I think I got it. Thank you!