Then why would Zod and his crew carry it on a ship of their own?
In this scene, divers find a rock on the shallow parts of the Southern Indian Ocean. This rock contained Kryptonite and at this point I'm assuming it came from the wreckage of the World Engine, which was part of Zod's ship.
Why would they carry a substance, which is clearly harmful for them, on their ship? Was it the energy source of the World Engine? What am I missing?