Is there a simple way to determine genuine ivory from imitation ivory? ?

Hold a lighter to the piece, you'll soon know by the smell.

Mike has the real answer - the standard test. More casually, real ivory (which is almost nonexistent on today's marketplace) has a grain just like wood. If you look closely, you can see darker and lighter striations in the material. Some has more, some has less, but it will be there. Plastic, which is all "imitation ivory" is, will be pure white all through. And plastic is lighter, too. If you're in some shop and you can't burn it......

Heat a needle and in an out of the way location on the piece, push the hot point in. Plastic will smell like burning plastic, ivory will smell like burned hair or leather

Fake ivory is going to be more porous than real ivory. You would need at least a jewlers loop if nothing else to tell the difference, but a Jeweler may be able to help you better.