Localization of injective modules over valuation rings
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- by François Couchot PDF
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Abstract:
It is proved that $E_J$ is injective if $E$ is an injective module over a valuation ring $R$, for each prime ideal $J\ne Z$. Moreover, if $E$ or $Z$ is flat, then $E_Z$ is injective, too. It follows that localizations of injective modules over h-local Prüfer domains are injective, too.References
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Additional Information
- François Couchot
- Affiliation: Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Département de Mathématiques et Mécanique, 14032 Caen cedex, France
- Email: couchot@math.unicaen.fr
- Received by editor(s): November 12, 2004
- Published electronically: October 5, 2005
- Communicated by: Bernd Ulrich
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1013-1017
- MSC (2000): Primary 13F30, 13C11
- DOI: https://doi.org/10.1090/S0002-9939-05-08350-4
- MathSciNet review: 2196032