ABSTRACT
Recall that an indecomposable rtffr group G has the refinement property if given a direct sum G(n) ∼= H ⊕H ′ of groups then H ∼= G(m) for some integer m > 0. We showed in Theorem 4.2.13 that if E(G) is a commutative ring then the indecomposable rtffr group G possesses the local refinement property. That is, given a direct sum G(n) ∼= H ⊕H ′ of groups then H ∼= G1 ⊕ · · · ⊕ Gm for some groups G1, . . . , Gm that are locally isomorphic to G. This brings two questions to mind.
