Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Localization of injective modules over valuation rings

Author: François Couchot
Journal: Proc. Amer. Math. Soc. 134 (2006), 1013-1017
MSC (2000): Primary 13F30, 13C11
Published electronically: October 5, 2005
MathSciNet review: 2196032
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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.

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François Couchot
Affiliation: Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Département de Mathématiques et Mécanique, 14032 Caen cedex, France

Keywords: Valuation ring, injective module, h-local domain, Pr\"ufer domain.
Received by editor(s): November 12, 2004
Published electronically: October 5, 2005
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society