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.