Summary
A module B over a commutative domain R is said to be a Baer module if Ext 1R (B, T)=0for all torsion R-modules T. The case in which R is an arbitrary valuation domain is investigated, and it is shown that in this case Baer modules are necessarily free. The method employed is totally different from Griffith's method for R=Z which breaks down for non-hereditary rings.
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This research was partially supported by NSF Grants DMS-8400451 and DMS-8500933.
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Eklof, P.C., Fuchs, L. Baer modules over valuation domains. Annali di Matematica pura ed applicata 150, 363–373 (1988). https://doi.org/10.1007/BF01761475
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DOI: https://doi.org/10.1007/BF01761475