Tests for injectivity of modules over commutative rings

Lars Winther Christensen, Srikanth B. Iyengar

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


It is proved that a module M over a commutative noetherian ring R is injective if ExtRi((R/p)p,M)=0 holds for every i⩾ 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 R(F, M) is injective and ExtRi(F,M)=0 for all i⩾ 1 is injective. A limited version of this characterization is also proved for certain non-noetherian rings.

Original languageEnglish
Pages (from-to)243-250
Number of pages8
JournalCollectanea Mathematica
Issue number2
StatePublished - May 1 2017


  • Cosupport
  • Injective dimension
  • Injective module


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