A refinement of Gorenstein flat dimension via the flat–cotorsion theory

Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson, Dejun Wu, Gang Yang

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological dimension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings—the setting where the Gorenstein flat dimension is known to behave as expected.

Original languageEnglish
Pages (from-to)346-370
Number of pages25
JournalJournal of Algebra
Volume567
DOIs
StatePublished - Feb 1 2021

Keywords

  • Flat-cotorsion module
  • Gorenstein flat dimension
  • Gorenstein flat-cotorsion dimension

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