Question
If $A$ and $B$ are ideals of a ring, show that the $s u m$ of $A$ and $B, A+B=$ $\{a+b \mid a \in A, b \in B\}$, is an ideal.
Step 1
First, we need to show that $A+B$ is non-empty. Since $A$ and $B$ are ideals, they both contain the additive identity $0$. Thus, $0+0=0 \in A+B$, so $A+B$ is non-empty. Show more…
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