On finitely injective modules and locally pure-injective modules over Prüfer domains

Salce, Luigi

doi:10.1090/S0002-9939-07-08906-X

On finitely injective modules and locally pure-injective modules over Prüfer domains
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Proc. Amer. Math. Soc. 135 (2007), 3485-3493 Request permission

Abstract:

Over Matlis valuation domains there exist finitely injective modules which are not direct sums of injective modules, as well as complete locally pure-injective modules which are not the completion of a direct sum of pure-injective modules. Over Prüfer domains which are either almost maximal, or $h$-local Matlis, finitely injective torsion modules and complete torsion-free locally pure-injective modules correspond to each other under the Matlis equivalence. Almost maximal Prüfer domains are characterized by the property that every torsion-free complete module is locally pure-injective. It is derived that semi-Dedekind domains are Dedekind.

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