AC-GORENSTEIN RINGS AND THEIR STABLE MODULE CATEGORIES
Abstrak
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.
Penulis (1)
JAMES GILLESPIE
Akses Cepat
- Tahun Terbit
- 2018
- Bahasa
- en
- Total Sitasi
- 7×
- Sumber Database
- CrossRef
- DOI
- 10.1017/s1446788718000290
- Akses
- Open Access ✓