Localization of Injective Modules Over Arithmetical Rings |
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| Authors: | François Couchot |
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| Institution: | 1. Département de Mathématiques et Mécanique , Laboratoire de Mathématiques Nicolas Oresme , Caen Cedex, France couchot@math.unicaen.fr |
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| Abstract: | 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 Prüfer domain of finite character, localizations of injective R-modules are injective. |
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| Keywords: | Arithmetical ring Finite character Finitely injective module FP-injective module Goldie dimension Injective module Prüfer domain Semicoherent ring Valuation ring |
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