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Torsion of injective modules and weakly pro-regular sequences

par Schenzel, Peter;Simon, Anne-Marie
Référence Communications in algebra, 48, 9, page (3637-3650)
Publication Publié, 2020-09-01

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Résumé :

Let R a commutative ring, (Formula presented.) an ideal, I an injective R-module and (Formula presented.) a multiplicatively closed set. When R is Noetherian it is well-known that the (Formula presented.) -torsion sub-module (Formula presented.) the factor module (Formula presented.) and the localization IS are again injective R-modules. We investigate these properties in the case of a commutative ring R by means of a notion of relatively- (Formula presented.) -injective R-modules. In particular we get another characterization of weakly pro-regular sequences in terms of relatively injective modules. Also we present examples of non-Noetherian commutative rings R and injective R-modules for which the previous properties do not hold. Moreover, under some weak pro-regularity conditions we obtain results of Mayer-Vietoris type.