Absolutely Clean, Level, and Gorenstein AC-Injective Complexes. Issue 5 (3rd May 2016)

• Record Type: Journal Article
• Authors: Bravo, Daniel; Gillespie, James
• Is Part Of: Communications in algebra. Volume 44:Issue 5(2016)
• Page Start: 2213
• Page End: 2233
• Publication Date: 2016-05-03
• Subjects: Chain complexes -- Gorenstein homological algebra -- Model structure; 18G35 -- 18G25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1044100
• Languages: English
• ISSNs: 0092-7872

Abstract

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.