The Ladder Construction of Pruefer Modules

Let R be a ring (associative, with 1). A non-zero module M is said to be a Pruefer module provided there exists a surjective, locally nilpotent endomorphism with kernel of finite length. The aim of this note is construct Pruefer modules starting from a pair of module homomorphisms w,v: U_0 -> U_1, where w is injective and its cokernel is of finite length.