TORSION FREE ABELIAN GROUPS QUASI-PROJECTIVE OVER THEIR ENDOMORPHISM RINGS II

Let R be a commutative ring with 1, and X an jβ-module. Then M = X 0 R is quasi-projective as an JS'-module, where E is either Hom z (M, M) or Hom ^ {M, M). In this note it is shown that any torsion free abelian group G of finite rank, quasi-projective over its endomorphism ring, is quasi-isomor-phic to X®R, where R is a direct sum of Dedekind domains and X is an iέ-module. Introduction * If R is a ring with identity, an JS-module M is said to be quasi-projective if for any submodule N of M, and jR-map f:M-+ M/N, there is an.β-map f: M-+M such that / followed by the factor map M —> M/N is equal to /. Results on quasi-projective modules appear in [3], [6], and [7]. In this note, we will be con