Abstract
Let F be the finite field of q elements and F[T] be the polynomial ring with one variale over F . We will study Drinfeld F[t]-modules of rank 2 over F(T) . Each such Drinfeld module gives a new F[T]-module structure on F(T) . It also induces a F[T]-module structure on F[T]/(P) for almost all irreducible polynomial P in F[T] . Our main purpose is to study the density of the monic irreducible polynomials in F[T] which make the induced F[T]-module on F[T]/(P) cyclic .