I'm curious if there is some sort of distributive law for ideals.
If $I,J,K$ are ideals in an arbitrary ring, does $I(J+K)=IJ+IK$?
The containment "$\subset$" is pretty clear I think. But the opposite ontainment doesn't feel like it should work. I couldn't work out a counterexample with ideals in $\mathbb{Z}$ however. So does such an equality always hold or not?