Injective modules under faithfully flat ring extensions

Lars Winther, Fatih Köksal

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let R be a commutative ring and let S be an R-algebra. It is wellknown that if N is an injective R-module, then HomR(S,N) is an injective S-module. The converse is not true, not even if R is a commutative noetherian local ring and S is its completion, but it is close: It is a special case of ourmain theorem that, in this setting, an R-module N with Ext>0 R (S,N) = 0 is injective if HomR(S,N) is an injective S-module.

Original languageEnglish
Pages (from-to)1015-1020
Number of pages6
JournalProceedings of the American Mathematical Society
Volume144
Issue number3
DOIs
StatePublished - Mar 2016

Keywords

  • Co-base change
  • Faithfully flat ring extension
  • Injective module

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