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

Author: Luigi Salce
Journal: Proc. Amer. Math. Soc. 135 (2007), 3485-3493
MSC (2000): Primary 13A05; Secondary 13C11, 13F05
Published electronically: 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 $ 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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Additional Information

Luigi Salce
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, via Trieste 63, I-35121 Padova, Italy

Keywords: Finitely injective modules, locally pure-injective modules, Matlis equivalence
Received by editor(s): February 6, 2006
Received by editor(s) in revised form: August 21, 2006
Published electronically: June 29, 2007
Additional Notes: The research of this author was supported by MIUR, PRIN 2005.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.