Definition:Sum of Ideals of Ring

Definition
Let $R$ be a ring.

Two ideals
Let $I$ and $J$ be ideals of $R$.

Their sum is the ideal equal to their subset sum:
 * $I + J = \set {i + j : i \in I \land j \in J}$

Also see

 * Sum of Ideals is Ideal
 * Definition:Product of Ideals of Ring

Generalizations

 * Definition:Generated Ideal of Ring, as shown at Sum of Ideals is Ideal Generated by Union
 * Definition:Subset Product