Non-commutative localisation and finite domination over strongly Z-graded rings

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Abstract

Let R=⨁∞k=−∞Rk be a strongly Z-graded ring, and let C+ be a chain complex of modules over the positive subring P=⨁∞k=0Rk. The complex C+⊕PR0 is contractible (resp., C+ is R0-finitely dominated) if and only if C+⊕PL is contractible, where L is a suitable non-commutative localisation of P. We exhibit universal properties of these localisations, and show by example that an R0-finitely dominated complex need not be P-homotopy finite.
Original languageEnglish
Pages (from-to)373-398
Number of pages26
JournalHomology, Homotopy and Applications
Volume24
Issue number1
DOIs
Publication statusPublished - 18 May 2022

ASJC Scopus subject areas

  • General Mathematics
  • Algebra and Number Theory

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