Localization of injective modules over valuation rings

Details Localization of injective modules over valuation rings Localization of injective modules over valuation rings

2005-10-04

arxiv.org/abs/math/0510074v2

Proceedings of the American Mathematical Society 134 (2006) 1013--1017

Mathematics

Rings and Algebras

Scientific paper

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 Pr\"{u}fer domains are injective too.

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