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Miklos Schweitzer 1968_1

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October 8, 2008
abstract algebrasuperior algebrasuperior algebra unsolved

Problem Statement

Consider the endomorphism ring of an Abelian torsion-free (resp. torsion) group G G. Prove that this ring is Neumann-regular if and only if G 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 R is called Neumann-regular if for every α∈R \alpha \in R there exists a β∈R \beta \in R such that \alpha \beta \alpha\equal{}\alpha.) E. Freid
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