The stable module category of a general ring
D Bravo, J Gillespie, M Hovey - arXiv preprint arXiv:1405.5768, 2014 - arxiv.org
D Bravo, J Gillespie, M Hovey
arXiv preprint arXiv:1405.5768, 2014•arxiv.orgFor any ring R we construct two triangulated categories, each admitting a functor from R-
modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or
Gorenstein ring, these triangulated categories agree with each other and with the usual
stable module category. Our stable module categories are homotopy categories of Quillen
model structures on the category of R-modules. These model categories involve
generalizations of Gorenstein projective and injective modules that we derive by replacing …
modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or
Gorenstein ring, these triangulated categories agree with each other and with the usual
stable module category. Our stable module categories are homotopy categories of Quillen
model structures on the category of R-modules. These model categories involve
generalizations of Gorenstein projective and injective modules that we derive by replacing …
For any ring R we construct two triangulated categories, each admitting a functor from R-modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or Gorenstein ring, these triangulated categories agree with each other and with the usual stable module category. Our stable module categories are homotopy categories of Quillen model structures on the category of R-modules. These model categories involve generalizations of Gorenstein projective and injective modules that we derive by replacing finitely presented modules by modules of type FP-infinity. Along the way, we extend the perfect duality between injective left modules and flat right modules that holds over Noetherian rings to general rings by considering weaker notions of injectivity and flatness.
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