Warfield duality and rank-one quasi-summands of tensor products of finite rank locally free modules over Dedekind domains (Q1823997)

If G and H are strongly indecomposable finite rank torsion free modules over a Dedekind domain and if A is a locally free rank-one quasi-summand of \(G\otimes H\), then G and H are also locally free t(A)-bounded with non-trivial traces and H is quasi-isomorphic to Hom(G,A). The adjointness isomorphism Hom(G\(\otimes H,A)\cong Hom(G,Hom(H,A))\) takes split quasi- epimorphisms to split quasi-monomorphisms. Some results of Warfield from 1968 are looked over in a new light.