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oai:recercat.cat:2072/3776502024-12-20T11:28:47Zcom_2072_199267com_2072_4427col_2072_199862

Tests for injectivity of modules over commutative rings Christensen, L.W. Iyengar, S.B. Matemàtiques 51 It is proved that a module $ M$ over a commutative noetherian ring $ R$ is injective if $ \mathrm{Ext}_{R}^{i}((R/{\mathfrak p})_{\mathfrak p},M)=0$ for every $ i\ge 1$ and every prime ideal $ \mathfrak{p}$ in~$ R$ . This leads to the following characterization of injective modules: If $ F$ is faithfully flat, then a module $ M$ such that $ \Hom_R(F,M)$ is injective and $ \Ext^i_R(F,M)=0$ for all $ i\ge 1$ is injective. A limited version of this characterization is also proved for certain non-noetherian rings. 2015-01-01 info:eu-repo/semantics/preprint http://hdl.handle.net/2072/377650 eng CRM Preprints L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess 13 p. application/pdf RECERCAT (Dipòsit de la Recerca de Catalunya)