Exercise 13, § 7

Let K be a commutative field of characteristic zero, and let A be the ring K[T]. Let $d$ be the derivation $\frac{d}{dT}$. Prove that the ring A[D] (Exercise 12) is quasi-simple. (Determine the derivations ad(D) and ad(T), and deduce that every nonzero two-sided ideal contains an invertible element.)