Absolutely Clean, Level, and Gorenstein AC-Injective Complexes. Issue 5 (3rd May 2016) - Bravo, Daniel; Gillespie, James
Abstract : Absolutely clean and level R -modules were introduced in [2 ] and used to show how Gorenstein homological algebra can be extended to an arbitrary ring R . This led to the notion of Gorenstein AC-injective and Gorenstein AC-projective R -modules. Here we study these concepts in the category of chain complexes of R -modules. We define, characterize and deduce properties of absolutely clean, level, Gorenstein AC-injective, and Gorenstein AC-projective chain complexes. We show that the category Ch( R ) of chain complexes has a cofibrantly generated model structure where every object is cofibrant and the fibrant objects are exactly the Gorenstein AC-injective chain complexes.