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AC-GORENSTEIN RINGS AND THEIR STABLE MODULE CATEGORIES

  • JAMES GILLESPIE (a1)
Abstract

We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of Gorenstein ring that is compatible with the Gorenstein AC-injective and Gorenstein AC-projective modules of Bravo–Gillespie–Hovey. It is also compatible with the notion of $n$ -coherent rings introduced by Bravo–Perez. So a $0$ -coherent AC-Gorenstein ring is precisely a usual Gorenstein ring in the sense of Iwanaga, while a $1$ -coherent AC-Gorenstein ring is precisely a Ding–Chen ring. We show that any AC-Gorenstein ring admits a stable module category that is compactly generated and is the homotopy category of two Quillen equivalent abelian model category structures. One is projective with cofibrant objects that are Gorenstein AC-projective modules while the other is an injective model structure with fibrant objects that are Gorenstein AC-injectives.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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