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arXiv · 1508.04639

Tests for injectivity of modules over commutative rings

Lars Winther Christensen·Srikanth B. Iyengar
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Abstract

It is proved that a module M over a commutative noetherian ring R is injective if Ext^i((R/p)_p,M)=0 holds for every i\ge 1 and every prime ideal p in R. This leads to the following characterization of injective modules: If F is faithfully flat, then a module M such that Hom(F,M) is injective and Ext^i(F,M)=0 for all i\ge 1 is injective. A limited version of this characterization is also proved for certain non-noetherian rings.

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Lars Winther Christensen, Srikanth B. Iyengar. 2015-08-19. Tests for injectivity of modules over commutative rings. https://arxiv.org/abs/1508.04639

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