how long can i keep fresh cooked green beans in the fridge...they have nothing on them except a little bit salt when cooking?

They lose their fresh flavor & color fairly quickly. You can eat them a day--maybe even 2--after cooking. They won't be as good as fresh, but they won't hurt you. More than that and I'd cut them up into salad. Finish them soon!
You can drizzle with olive oil and minced garlic mashed with salt, some finely chopped cilantro, and add a little lemon juice just before serving.

Exactly as boulangere says! Any more than two days, the flavors and the vitamins start to break down.

A couple of days at best. Once they've been cooked, even slightly, they begin to break down pretty quickly. Use them on salads, dip them into salsa, eat 'em up!