## When are principal ideals prime ideals?

I can't seem to figure this one out...

Under the operation that A*B is the intersection of A and B, consider the principal ideal <A>. For which subsets A of X is the ideal <A> a prime ideal?

(this is also the boolean ring where A + B = set of elements in union of A and B but not in intersection of A and B. i'm not sure if this matters?