Localization of injective modules over arithmetical rings
Rings and Algebras
2009-01-13 v1
Abstract
It is proved that localizations of injective -modules of finite Goldie dimension are injective if is an arithmetical ring satisfying the following condition: for every maximal ideal , is either coherent or not semicoherent. If, in addition, each finitely generated -module has finite Goldie dimension, then localizations of finitely injective -modules are finitely injective too. Moreover, if is a Pr\"ufer domain of finite character, localizations of injective -modules are injective.
Cite
@article{arxiv.0901.1560,
title = {Localization of injective modules over arithmetical rings},
author = {Francois Couchot},
journal= {arXiv preprint arXiv:0901.1560},
year = {2009}
}