Localization of injective modules over arithmetical rings

Details Localization of injective modules over arithmetical rings Localization of injective modules over arithmetical rings

2009-01-12

arxiv.org/abs/0901.1560v1

Mathematics

Rings and Algebras

Scientific paper

It is proved that localizations of injective $R$-modules of finite Goldie dimension are injective if $R$ is an arithmetical ring satisfying the following condition: for every maximal ideal $P$, $R_P$ is either coherent or not semicoherent. If, in addition, each finitely generated $R$-module has finite Goldie dimension, then localizations of finitely injective $R$-modules are finitely injective too. Moreover, if $R$ is a Pr\"ufer domain of finite character, localizations of injective $R$-modules are injective.

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