The Divisible and E-Injective Hulls of a Torsion Free Group

  • C. Vinsonhaler
Part of the International Centre for Mechanical Sciences book series (CISM, volume 287)


Recently there has been considerable interest in the structure of torsion free abelian groups G as modules over their endomorphism rings E = End(G). In particular, homological properties of the E-module G have been the focus of a number of papers (see (2), (7), (8)). In (2) the structure of finite rank groups G such that G was E-projective was determined, while in (7) the injective hull of G as an E-module was investigated. In the latter paper the question was asked: For which groups G is the E-injective hull of G equal to QG, the divisible hull? This is equivalent to the question: When is QG injective as a QE-module? In this note we obtain a partial answer by imposing an additional condition on G. We examine groups G for which QG is injective as a QE-module and HomQE(QG, QG) = Q(center E). This property, called aEqi, is equivalent to condition weaker than quasi-injectivuty on EG.


Abelian Group Endomorphism Ring Finite Rank Torsion Free Group Jacobson Radical 
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Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • C. Vinsonhaler
    • 1
  1. 1.University of ConnecticutStorrsUSA

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