Sum of two ideals $I=<a,b>, J=<c,d>$.

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Sum of ideals $I_j$ is defined by $\sum_{j \in J} I_j=<\cup_{j \in J} I_j>$. I'm not really sure how to use this definition in, for example, sum of ideals $I=<a,b>, J=<c,d>$. How should I write it? Thank you.

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$ I + J =\ <a, b, c, d>$.