2014/08/29 by Daniel Bravo, James Gillespie, Bravo, Daniel +1
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1408.7089
openalex publication_date 2014/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Absolutely clean and level R-modules were introduced in [BGH13] 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.