Gorenstein dimensions of unbounded complexes and change of base (with an appendix by Driss Bennis)

Lars Winther Christensen, Fatih Köksal, Li Liang

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S ⊗RM is Gorenstein flat, and that an R-module N is Gorenstein injective if and only if it is cotorsion and the left S-module HomR(S,N) is Gorenstein injective. We apply these results to the study of Gorenstein homological dimensions of unbounded complexes. In particular, we prove two theorems on stability of these dimensions under faithfully flat (co-)base change.

Original languageEnglish
Pages (from-to)401-420
Number of pages20
JournalScience China Mathematics
Volume60
Issue number3
DOIs
StatePublished - Mar 1 2017

Keywords

  • Gorenstein flat dimension
  • Gorenstein injective dimension
  • faithfully flat base change
  • faithfully flat co-base change

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