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 Pruefer domains which are either almost maximal, or h-local Matlis, finitely injective torsion modules and complete torsionfree locally pure-injective modules correspond to each others under the Matlis equivalence. Almost maximal Pruefer domains are characterized by the property that every torsionfree complete module is locally pure-injective. It is derived that semi-Dedekind domains are Dedekind.

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

SALCE, LUIGI
2007

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 Pruefer domains which are either almost maximal, or h-local Matlis, finitely injective torsion modules and complete torsionfree locally pure-injective modules correspond to each others under the Matlis equivalence. Almost maximal Pruefer domains are characterized by the property that every torsionfree complete module is locally pure-injective. It is derived that semi-Dedekind domains are Dedekind.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1776469
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