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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Luigi Salce
Journal: Proc. Amer. Math. Soc. 135 (2007), 3485-3493.
MSC (2000): Primary 13A05; Secondary 13C11, 13F05
Posted: June 29, 2007
MathSciNet review: 2336561
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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 -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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