Warfield duality and rank-one quasi-summands of tensor products of finite rank locally free modules over Dedekind domains. (English) Zbl 0682.13001
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.
Reviewer: R.M.Dimitrić
MSC:
13C05 | Structure, classification theorems for modules and ideals in commutative rings |
13C13 | Other special types of modules and ideals in commutative rings |
13F05 | Dedekind, Prüfer, Krull and Mori rings and their generalizations |
References:
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