Localization of injective modules over valuation rings

Francois Couchot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

It is proved that the localization of an injective module E, over a valuation ring R, at a prime ideal J, is injective if J is not the subset of zero-divisors of R or if J or E is flat. It follows that localizations of injective modules over h-local Prüfer domains are injective too.

Mots clés: valuation ring; injective module; h-local domain; Prüfer domain

Domaines: Anneaux et algèbres [math.RA]

Francois Couchot. Localization of injective modules over valuation rings. Proceedings of the American Mathematical Society, 2006, 134, pp.1013--1017. ⟨hal-00009475v2⟩