A nonempty set in a ring is called an ideal if
(1) it is closed under addition:
(2) it "swallows up" under multiplication: .
A proper ideal is one that is not equal to the entire ring.
A proper ideal is prime if implies that or .
A proper ideal is maximal if there are no ideals in between it and the entire ring: if is an ideal, then implies or .
How many ideals of are prime but not maximal?