Heat olive oil in a saucepan over medium heat. Finely chop the onion, garlic and grated ginger and gently fry it until onions are soft. Be careful not to burn the garlic - add a little water if necessary.
Chop the tomatoes and add to pan with onions. Cook for 3 minutes. Stir in chopped arugula and cook until wilted - 1 to 2 minutes.
Add the sliced green olives and remove from the heat, then season.
Cook the Spaghetti in plenty of salted water, drain and toss with the tomato-arugula sauce.