Let R be a ring with a multiplicative identity. If U is an additive subgroup of R such that ur in U for all u in U and for all r in R, then U is said to be a right ideal of R. If R has exactly two right ideals, which of the following must be true?
I. R is commutative.
II. R is a division ring (that is, all elements except the additive identity have multiplicative inverses).
III. R is infinite.
(A)I only (B)II only (C)III only (D)I and II only
B