Consider the endomorphism ring of an Abelian torsion-free (resp. torsion) group G. Prove that this ring is Neumann-regular if and only if G is a discrete direct sum of groups isomorphic to the additive group of the rationals (resp. ,a discrete direct sum of cyclic groups of prime order). (A ring R is called Neumann-regular if for every α∈R there exists a β∈R such that \alpha \beta \alpha\equal{}\alpha.)
E. Freid abstract algebrasuperior algebrasuperior algebra unsolved