No, is it to a power of a prime? No it is not.

A field has no ideal, since this is it not a field it might.So a list of all its ideals would be 0 and all the elements in Z60.

(Note: I worked on this problem before when you posted it and it got a little messy by looking at all the possible ideal. What I was doing was finding all the cyclic subgorups of this ring because they need to be cyclic for the additive group is cylcic)

NoIs this correct?

I think you mean when you have a ring homomorphism the image of is a homomorphic image.And could someone just explain quickly what a homomorphic image is?